LMFDB - Embedded newform 825.2.n.p.751.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [825,2,Mod(301,825)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(825, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("825.301"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$825 = 3 \cdot 5^{2} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	825.n (of order $5$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [24,2,-6,-6,0,2,4,6,-6,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			751.1
Character	$\chi$	$=$	825.751
Dual form			825.2.n.p.301.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.91233 + 1.38939i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.10857 - 3.41183i) q^{4} +(-1.91233 - 1.38939i) q^{6} +(-0.529727 + 1.63033i) q^{7} +(1.15951 + 3.56862i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.406668 - 3.29160i) q^{11} +3.58741 q^{12} +(2.85857 - 2.07687i) q^{13} +(-1.25215 - 3.85373i) q^{14} +(-1.37103 - 0.996109i) q^{16} +(0.302010 + 0.219423i) q^{17} +(0.730445 - 2.24808i) q^{18} +(-1.78239 - 5.48564i) q^{19} -1.71423 q^{21} +(5.35099 + 5.72960i) q^{22} -3.80745 q^{23} +(-3.03565 + 2.20553i) q^{24} +(-2.58094 + 7.94332i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(4.97517 + 3.61467i) q^{28} +(-1.08672 + 3.34458i) q^{29} +(8.16928 - 5.93533i) q^{31} -3.49870 q^{32} +(3.00483 - 1.40392i) q^{33} -0.882407 q^{34} +(1.10857 + 3.41183i) q^{36} +(3.56666 - 10.9770i) q^{37} +(11.0302 + 8.01391i) q^{38} +(2.85857 + 2.07687i) q^{39} +(-0.747505 - 2.30059i) q^{41} +(3.27818 - 2.38174i) q^{42} -0.224486 q^{43} +(-11.6812 - 2.26149i) q^{44} +(7.28109 - 5.29002i) q^{46} +(-1.44508 - 4.44749i) q^{47} +(0.523685 - 1.61174i) q^{48} +(3.28575 + 2.38724i) q^{49} +(-0.115358 + 0.355034i) q^{51} +(-3.91700 - 12.0553i) q^{52} +(1.97737 - 1.43665i) q^{53} +2.36377 q^{54} -6.43226 q^{56} +(4.66636 - 3.39031i) q^{57} +(-2.56876 - 7.90582i) q^{58} +(1.65630 - 5.09757i) q^{59} +(2.75575 + 2.00217i) q^{61} +(-7.37587 + 22.7006i) q^{62} +(-0.529727 - 1.63033i) q^{63} +(9.43272 - 6.85327i) q^{64} +(-3.79563 + 6.85964i) q^{66} +9.08988 q^{67} +(1.08343 - 0.787161i) q^{68} +(-1.17657 - 3.62110i) q^{69} +(7.09964 + 5.15819i) q^{71} +(-3.03565 - 2.20553i) q^{72} +(-4.62358 + 14.2299i) q^{73} +(8.43076 + 25.9472i) q^{74} -20.6919 q^{76} +(5.58182 + 1.08064i) q^{77} -8.35211 q^{78} +(-7.11291 + 5.16783i) q^{79} +(0.309017 - 0.951057i) q^{81} +(4.62589 + 3.36090i) q^{82} +(-6.02082 - 4.37438i) q^{83} +(-1.90035 + 5.84866i) q^{84} +(0.429291 - 0.311898i) q^{86} -3.51670 q^{87} +(11.2749 - 5.26790i) q^{88} +15.5058 q^{89} +(1.87173 + 5.76059i) q^{91} +(-4.22082 + 12.9903i) q^{92} +(8.16928 + 5.93533i) q^{93} +(8.94275 + 6.49729i) q^{94} +(-1.08116 - 3.32746i) q^{96} +(-11.8632 + 8.61910i) q^{97} -9.60024 q^{98} +(2.26375 + 2.42393i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$24 q + 2 q^{2} - 6 q^{3} - 6 q^{4} + 2 q^{6} + 4 q^{7} + 6 q^{8} - 6 q^{9} + 24 q^{12} + 4 q^{13} + 2 q^{14} - 22 q^{16} + 4 q^{17} + 2 q^{18} + 8 q^{19} - 16 q^{21} - 4 q^{22} + 6 q^{24} - 38 q^{26} - 6 q^{27}+ \cdots - 120 q^{98}+O(q^{100})$ 24 * q + 2 * q^2 - 6 * q^3 - 6 * q^4 + 2 * q^6 + 4 * q^7 + 6 * q^8 - 6 * q^9 + 24 * q^12 + 4 * q^13 + 2 * q^14 - 22 * q^16 + 4 * q^17 + 2 * q^18 + 8 * q^19 - 16 * q^21 - 4 * q^22 + 6 * q^24 - 38 * q^26 - 6 * q^27 + 30 * q^28 - 10 * q^31 - 56 * q^32 + 10 * q^33 + 12 * q^34 - 6 * q^36 + 10 * q^37 + 4 * q^38 + 4 * q^39 + 30 * q^41 - 8 * q^42 - 64 * q^43 + 24 * q^44 + 54 * q^46 - 8 * q^47 - 2 * q^48 + 14 * q^49 + 14 * q^51 + 14 * q^52 + 26 * q^53 - 8 * q^54 + 12 * q^56 + 8 * q^57 + 20 * q^58 - 30 * q^59 + 20 * q^61 - 50 * q^62 + 4 * q^63 - 32 * q^64 + 6 * q^66 + 20 * q^67 - 62 * q^68 - 10 * q^69 - 16 * q^71 + 6 * q^72 - 12 * q^73 + 16 * q^74 - 68 * q^76 - 2 * q^77 + 32 * q^78 + 26 * q^79 - 6 * q^81 + 56 * q^82 + 48 * q^83 - 52 * q^86 + 48 * q^88 - 20 * q^89 - 20 * q^91 + 46 * q^92 - 10 * q^93 - 36 * q^94 + 14 * q^96 - 14 * q^97 - 120 * q^98

Character values

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

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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

)

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

$2$	−1.91233	+	1.38939i	−1.35222	+	0.982446i	−0.353324	+	0.935501i	$0.614949\pi$
$2$	−1.91233	+	1.38939i	−1.35222	+	0.982446i	−0.998897	+	0.0469455i	$0.985051\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	1.10857	−	3.41183i	0.554285	−	1.70591i
$5$		0			0
$5$		0			0
$6$	−1.91233	−	1.38939i	−0.780705	−	0.567216i
$7$	−0.529727	+	1.63033i	−0.200218	+	0.616207i	0.799658	+	0.600456i	$0.205014\pi$
$7$	−0.529727	+	1.63033i	−0.200218	+	0.616207i	−0.999876	+	0.0157517i	$0.994986\pi$
$8$	1.15951	+	3.56862i	0.409950	+	1.26170i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	−0.406668	−	3.29160i	−0.122615	−	0.992454i
$11$	−0.406668	−	3.29160i	−0.122615	−	0.992454i
$12$	3.58741			1.03560
$13$	2.85857	−	2.07687i	0.792824	−	0.576020i	−0.115976	−	0.993252i	$-0.537000\pi$
$13$	2.85857	−	2.07687i	0.792824	−	0.576020i	0.908800	+	0.417232i	$0.137000\pi$
$14$	−1.25215	−	3.85373i	−0.334652	−	1.02995i
$15$		0			0
$16$	−1.37103	−	0.996109i	−0.342757	−	0.249027i
$17$	0.302010	+	0.219423i	0.0732482	+	0.0532180i	0.623807	−	0.781579i	$-0.285585\pi$
$17$	0.302010	+	0.219423i	0.0732482	+	0.0532180i	−0.550559	+	0.834797i	$0.685585\pi$
$18$	0.730445	−	2.24808i	0.172168	−	0.529877i
$19$	−1.78239	−	5.48564i	−0.408909	−	1.25849i	−0.917587	−	0.397535i	$-0.869866\pi$
$19$	−1.78239	−	5.48564i	−0.408909	−	1.25849i	0.508679	−	0.860956i	$-0.330134\pi$
$20$		0			0
$21$	−1.71423			−0.374076
$22$	5.35099	+	5.72960i	1.14084	+	1.22156i
$23$	−3.80745			−0.793907			−0.396954	−	0.917839i	$-0.629933\pi$
$23$	−3.80745			−0.793907			−0.396954	+	0.917839i	$0.629933\pi$
$24$	−3.03565	+	2.20553i	−0.619649	+	0.450201i
$25$		0			0
$26$	−2.58094	+	7.94332i	−0.506165	+	1.55781i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	4.97517	+	3.61467i	0.940219	+	0.683109i
$29$	−1.08672	+	3.34458i	−0.201799	+	0.621073i	0.798031	+	0.602617i	$0.205875\pi$
$29$	−1.08672	+	3.34458i	−0.201799	+	0.621073i	−0.999830	+	0.0184562i	$0.994125\pi$
$30$		0			0
$31$	8.16928	−	5.93533i	1.46725	−	1.06602i	0.485845	−	0.874045i	$-0.338512\pi$
$31$	8.16928	−	5.93533i	1.46725	−	1.06602i	0.981401	−	0.191971i	$-0.0614880\pi$
$32$	−3.49870			−0.618488
$33$	3.00483	−	1.40392i	0.523074	−	0.244392i
$34$	−0.882407			−0.151332
$35$		0			0
$36$	1.10857	+	3.41183i	0.184762	+	0.568638i
$37$	3.56666	−	10.9770i	0.586355	−	1.80462i	−0.00740399	−	0.999973i	$-0.502357\pi$
$37$	3.56666	−	10.9770i	0.586355	−	1.80462i	0.593759	−	0.804643i	$-0.297643\pi$
$38$	11.0302	+	8.01391i	1.78933	+	1.30003i
$39$	2.85857	+	2.07687i	0.457737	+	0.332565i
$40$		0			0
$41$	−0.747505	−	2.30059i	−0.116741	−	0.359291i	0.875565	−	0.483100i	$-0.160489\pi$
$41$	−0.747505	−	2.30059i	−0.116741	−	0.359291i	−0.992306	+	0.123809i	$0.960489\pi$
$42$	3.27818	−	2.38174i	0.505834	−	0.367510i
$43$	−0.224486			−0.0342338			−0.0171169	−	0.999853i	$-0.505449\pi$
$43$	−0.224486			−0.0342338			−0.0171169	+	0.999853i	$0.505449\pi$
$44$	−11.6812	−	2.26149i	−1.76101	−	0.340932i
$45$		0			0
$46$	7.28109	−	5.29002i	1.07354	−	0.779971i
$47$	−1.44508	−	4.44749i	−0.210786	−	0.648733i	−0.999426	−	0.0338775i	$-0.989214\pi$
$47$	−1.44508	−	4.44749i	−0.210786	−	0.648733i	0.788640	−	0.614855i	$-0.210786\pi$
$48$	0.523685	−	1.61174i	0.0755875	−	0.232634i
$49$	3.28575	+	2.38724i	0.469393	+	0.341034i
$50$		0			0
$51$	−0.115358	+	0.355034i	−0.0161533	+	0.0497147i
$52$	−3.91700	−	12.0553i	−0.543191	−	1.67177i
$53$	1.97737	−	1.43665i	0.271613	−	0.197339i	−0.443638	−	0.896206i	$-0.646312\pi$
$53$	1.97737	−	1.43665i	0.271613	−	0.197339i	0.715251	+	0.698868i	$0.246312\pi$
$54$	2.36377			0.321668
$55$		0			0
$56$	−6.43226			−0.859547
$57$	4.66636	−	3.39031i	0.618074	−	0.449057i
$58$	−2.56876	−	7.90582i	−0.337294	−	1.03808i
$59$	1.65630	−	5.09757i	0.215632	−	0.663648i	−0.783476	−	0.621422i	$-0.786555\pi$
$59$	1.65630	−	5.09757i	0.215632	−	0.663648i	0.999108	−	0.0422255i	$-0.0134448\pi$
$60$		0			0
$61$	2.75575	+	2.00217i	0.352838	+	0.256352i	0.750058	−	0.661371i	$-0.230025\pi$
$61$	2.75575	+	2.00217i	0.352838	+	0.256352i	−0.397221	+	0.917723i	$0.630025\pi$
$62$	−7.37587	+	22.7006i	−0.936737	+	2.88298i
$63$	−0.529727	−	1.63033i	−0.0667393	−	0.205402i
$64$	9.43272	−	6.85327i	1.17909	−	0.856659i
$65$		0			0
$66$	−3.79563	+	6.85964i	−0.467210	+	0.844364i
$67$	9.08988			1.11051			0.555253	−	0.831682i	$-0.312621\pi$
$67$	9.08988			1.11051			0.555253	+	0.831682i	$0.312621\pi$
$68$	1.08343	−	0.787161i	0.131386	−	0.0954573i
$69$	−1.17657	−	3.62110i	−0.141642	−	0.435929i
$70$		0			0
$71$	7.09964	+	5.15819i	0.842572	+	0.612165i	0.923088	−	0.384589i	$-0.125657\pi$
$71$	7.09964	+	5.15819i	0.842572	+	0.612165i	−0.0805158	+	0.996753i	$0.525657\pi$
$72$	−3.03565	−	2.20553i	−0.357755	−	0.259924i
$73$	−4.62358	+	14.2299i	−0.541150	+	1.66549i	0.188823	+	0.982011i	$0.439533\pi$
$73$	−4.62358	+	14.2299i	−0.541150	+	1.66549i	−0.729973	+	0.683476i	$0.760467\pi$
$74$	8.43076	+	25.9472i	0.980056	+	3.01630i
$75$		0			0
$76$	−20.6919			−2.37353
$77$	5.58182	+	1.08064i	0.636107	+	0.123151i
$78$	−8.35211			−0.945690
$79$	−7.11291	+	5.16783i	−0.800265	+	0.581426i	−0.910992	−	0.412425i	$-0.864682\pi$
$79$	−7.11291	+	5.16783i	−0.800265	+	0.581426i	0.110727	+	0.993851i	$0.464682\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	4.62589	+	3.36090i	0.510844	+	0.371150i
$83$	−6.02082	−	4.37438i	−0.660871	−	0.480151i	0.206086	−	0.978534i	$-0.433927\pi$
$83$	−6.02082	−	4.37438i	−0.660871	−	0.480151i	−0.866957	+	0.498383i	$0.833927\pi$
$84$	−1.90035	+	5.84866i	−0.207345	+	0.638142i
$85$		0			0
$86$	0.429291	−	0.311898i	0.0462916	−	0.0336328i
$87$	−3.51670			−0.377030
$88$	11.2749	−	5.26790i	1.20191	−	0.561560i
$89$	15.5058			1.64361			0.821806	−	0.569767i	$-0.192966\pi$
$89$	15.5058			1.64361			0.821806	+	0.569767i	$0.192966\pi$
$90$		0			0
$91$	1.87173	+	5.76059i	0.196210	+	0.603874i
$92$	−4.22082	+	12.9903i	−0.440051	+	1.35434i
$93$	8.16928	+	5.93533i	0.847115	+	0.615465i
$94$	8.94275	+	6.49729i	0.922375	+	0.670144i
$95$		0			0
$96$	−1.08116	−	3.32746i	−0.110345	−	0.339607i
$97$	−11.8632	+	8.61910i	−1.20452	+	0.875137i	−0.994722	−	0.102608i	$-0.967281\pi$
$97$	−11.8632	+	8.61910i	−1.20452	+	0.875137i	−0.209800	+	0.977744i	$0.567281\pi$
$98$	−9.60024			−0.969770
$99$	2.26375	+	2.42393i	0.227516	+	0.243614i
$100$		0			0
$101$	−4.96307	+	3.60588i	−0.493844	+	0.358798i	−0.806661	−	0.591015i	$-0.798727\pi$
$101$	−4.96307	+	3.60588i	−0.493844	+	0.358798i	0.312817	+	0.949813i	$0.398727\pi$
$102$	−0.272679	−	0.839219i	−0.0269992	−	0.0830951i
$103$	2.43193	−	7.48471i	0.239625	−	0.737490i	−0.756849	−	0.653590i	$-0.773262\pi$
$103$	2.43193	−	7.48471i	0.239625	−	0.737490i	0.996474	−	0.0839005i	$-0.0267378\pi$
$104$	10.7261	+	7.79298i	1.05178	+	0.764164i
$105$		0			0
$106$	−1.78533	+	5.49468i	−0.173407	+	0.533691i
$107$	−1.53155	−	4.71361i	−0.148060	−	0.455682i	0.849332	−	0.527859i	$-0.177005\pi$
$107$	−1.53155	−	4.71361i	−0.148060	−	0.455682i	−0.997392	+	0.0721774i	$0.977005\pi$
$108$	−2.90227	+	2.10863i	−0.279271	+	0.202903i
$109$	−2.61667			−0.250632			−0.125316	−	0.992117i	$-0.539994\pi$
$109$	−2.61667			−0.250632			−0.125316	+	0.992117i	$0.539994\pi$
$110$		0			0
$111$	11.5420			1.09551
$112$	2.35026	−	1.70756i	0.222078	−	0.161349i
$113$	−0.654058	−	2.01298i	−0.0615286	−	0.189366i	0.915567	−	0.402165i	$-0.131742\pi$
$113$	−0.654058	−	2.01298i	−0.0615286	−	0.189366i	−0.977096	+	0.212799i	$0.931742\pi$
$114$	−4.21316	+	12.9668i	−0.394599	+	1.21445i
$115$		0			0
$116$	10.2064	+	7.41540i	0.947643	+	0.688503i
$117$	−1.09188	+	3.36045i	−0.100944	+	0.310673i
$118$	3.91512	+	12.0495i	0.360416	+	1.10925i
$119$	−0.517715	+	0.376142i	−0.0474589	+	0.0344809i
$120$		0			0
$121$	−10.6692	+	2.67717i	−0.969931	+	0.243379i
$122$	−8.05170			−0.728966
$123$	1.95699	−	1.42184i	0.176456	−	0.128203i
$124$	−11.1941	−	34.4519i	−1.00526	−	3.09387i
$125$		0			0
$126$	3.27818	+	2.38174i	0.292043	+	0.212182i
$127$	9.66586	+	7.02266i	0.857707	+	0.623160i	0.927260	−	0.374418i	$-0.122157\pi$
$127$	9.66586	+	7.02266i	0.857707	+	0.623160i	−0.0695535	+	0.997578i	$0.522157\pi$
$128$	−6.35430	+	19.5565i	−0.561646	+	1.72857i
$129$	−0.0693699	−	0.213499i	−0.00610768	−	0.0187975i
$130$		0			0
$131$	20.3359			1.77676			0.888380	−	0.459110i	$-0.151831\pi$
$131$	20.3359			1.77676			0.888380	+	0.459110i	$0.151831\pi$
$132$	−1.45888	−	11.8083i	−0.126980	−	1.02778i
$133$	9.88758			0.857362
$134$	−17.3829	+	12.6294i	−1.50165	+	1.09101i
$135$		0			0
$136$	−0.432853	+	1.33218i	−0.0371168	+	0.114234i
$137$	4.29866	+	3.12316i	0.367259	+	0.266829i	0.756073	−	0.654487i	$-0.227115\pi$
$137$	4.29866	+	3.12316i	0.367259	+	0.266829i	−0.388814	+	0.921316i	$0.627115\pi$
$138$	7.28109	+	5.29002i	0.619808	+	0.450317i
$139$	4.08383	−	12.5688i	0.346386	−	1.06607i	−0.614451	−	0.788955i	$-0.710622\pi$
$139$	4.08383	−	12.5688i	0.346386	−	1.06607i	0.960837	−	0.277113i	$-0.0893775\pi$
$140$		0			0
$141$	3.78326	−	2.74870i	0.318608	−	0.231482i
$142$	−20.7436			−1.74076
$143$	−7.99871	−	8.56466i	−0.668886	−	0.716213i
$144$	1.69468			0.141223
$145$		0			0
$146$	−10.9291	−	33.6363i	−0.904498	−	2.78376i
$147$	−1.25504	+	3.86263i	−0.103514	+	0.318584i
$148$	−33.4979	−	24.3377i	−2.75351	−	2.00054i
$149$	4.90495	+	3.56366i	0.401830	+	0.291946i	0.770286	−	0.637699i	$-0.220114\pi$
$149$	4.90495	+	3.56366i	0.401830	+	0.291946i	−0.368456	+	0.929645i	$0.620114\pi$
$150$		0			0
$151$	−2.26661	−	6.97591i	−0.184454	−	0.567692i	0.815484	−	0.578779i	$-0.196471\pi$
$151$	−2.26661	−	6.97591i	−0.184454	−	0.567692i	−0.999939	+	0.0110874i	$0.996471\pi$
$152$	17.5094	−	12.7213i	1.42020	−	1.03184i
$153$	−0.373305			−0.0301799
$154$	−12.1757	+	5.68877i	−0.981147	+	0.458414i
$155$		0			0
$156$	10.2548	−	7.45058i	0.821045	−	0.596524i
$157$	−3.26192	−	10.0392i	−0.260329	−	0.801212i	−0.992733	−	0.120340i	$-0.961601\pi$
$157$	−3.26192	−	10.0392i	−0.260329	−	0.801212i	0.732403	−	0.680871i	$-0.238399\pi$
$158$	6.42210	−	19.7652i	0.510915	−	1.57243i
$159$	1.97737	+	1.43665i	0.156816	+	0.113933i
$160$		0			0
$161$	2.01691	−	6.20740i	0.158954	−	0.489211i
$162$	0.730445	+	2.24808i	0.0573892	+	0.176626i
$163$	8.17677	−	5.94077i	0.640454	−	0.465317i	−0.219552	−	0.975601i	$-0.570460\pi$
$163$	8.17677	−	5.94077i	0.640454	−	0.465317i	0.860006	+	0.510284i	$0.170460\pi$
$164$	−8.67786			−0.677627
$165$		0			0
$166$	17.5915			1.36537
$167$	10.7981	−	7.84529i	0.835583	−	0.607087i	−0.0855502	−	0.996334i	$-0.527265\pi$
$167$	10.7981	−	7.84529i	0.835583	−	0.607087i	0.921133	+	0.389247i	$0.127265\pi$
$168$	−1.98768	−	6.11744i	−0.153353	−	0.471971i
$169$	−0.159206	+	0.489985i	−0.0122466	+	0.0376911i
$170$		0			0
$171$	4.66636	+	3.39031i	0.356845	+	0.259263i
$172$	−0.248858	+	0.765907i	−0.0189753	+	0.0583999i
$173$	−5.51914	−	16.9862i	−0.419613	−	1.29144i	−0.908059	−	0.418841i	$-0.862436\pi$
$173$	−5.51914	−	16.9862i	−0.419613	−	1.29144i	0.488447	−	0.872594i	$-0.337564\pi$
$174$	6.72509	−	4.88606i	0.509828	−	0.370411i
$175$		0			0
$176$	−2.72124	+	4.91795i	−0.205121	+	0.370705i
$177$	5.35991			0.402875
$178$	−29.6522	+	21.5436i	−2.22253	+	1.61476i
$179$	−3.93601	−	12.1138i	−0.294192	−	0.905428i	−0.983492	−	0.180953i	$-0.942082\pi$
$179$	−3.93601	−	12.1138i	−0.294192	−	0.905428i	0.689300	−	0.724476i	$-0.257918\pi$
$180$		0			0
$181$	−16.7562	−	12.1741i	−1.24548	−	0.904891i	−0.247525	−	0.968882i	$-0.579617\pi$
$181$	−16.7562	−	12.1741i	−1.24548	−	0.904891i	−0.997950	+	0.0639909i	$0.979617\pi$
$182$	−11.5831	−	8.41558i	−0.858593	−	0.623805i
$183$	−1.05260	+	3.23958i	−0.0778106	+	0.239477i
$184$	−4.41479	−	13.5873i	−0.325463	−	1.00167i
$185$		0			0
$186$	−23.8688			−1.75015
$187$	0.599435	−	1.08333i	0.0438351	−	0.0792208i
$188$	−16.7760			−1.22352
$189$	1.38684	−	1.00760i	0.100878	−	0.0732921i
$190$		0			0
$191$	−1.91577	+	5.89614i	−0.138620	+	0.426630i	−0.996136	−	0.0878289i	$-0.972007\pi$
$191$	−1.91577	+	5.89614i	−0.138620	+	0.426630i	0.857515	+	0.514459i	$0.172007\pi$
$192$	9.43272	+	6.85327i	0.680748	+	0.494592i
$193$	4.46870	+	3.24670i	0.321664	+	0.233703i	0.736885	−	0.676018i	$-0.236296\pi$
$193$	4.46870	+	3.24670i	0.321664	+	0.233703i	−0.415221	+	0.909721i	$0.636296\pi$
$194$	10.7110	−	32.9651i	0.769006	−	2.36676i
$195$		0			0
$196$	11.7873	−	8.56399i	0.841952	−	0.611714i
$197$	−12.8524			−0.915693			−0.457846	−	0.889031i	$-0.651379\pi$
$197$	−12.8524			−0.915693			−0.457846	+	0.889031i	$0.651379\pi$
$198$	−7.69682	−	1.49011i	−0.546989	−	0.105898i
$199$	3.42830			0.243026			0.121513	−	0.992590i	$-0.461225\pi$
$199$	3.42830			0.243026			0.121513	+	0.992590i	$0.461225\pi$
$200$		0			0
$201$	2.80893	+	8.64499i	0.198126	+	0.609771i
$202$	4.48105	−	13.7913i	0.315286	−	0.970350i
$203$	−4.87711	−	3.54343i	−0.342306	−	0.248700i
$204$	1.08343	+	0.787161i	0.0758555	+	0.0551123i
$205$		0			0
$206$	5.74852	+	17.6921i	0.400518	+	1.23267i
$207$	3.08029	−	2.23796i	0.214095	−	0.155549i
$208$	−5.98796			−0.415190
$209$	−17.3317	+	8.09775i	−1.19886	+	0.560133i
$210$		0			0
$211$	−14.4241	+	10.4797i	−0.992996	+	0.721454i	−0.960575	−	0.278020i	$-0.910322\pi$
$211$	−14.4241	+	10.4797i	−0.992996	+	0.721454i	−0.0324211	+	0.999474i	$0.510322\pi$
$212$	−2.70953	−	8.33908i	−0.186091	−	0.572731i
$213$	−2.71182	+	8.34613i	−0.185811	+	0.571867i
$214$	9.47786	+	6.88607i	0.647893	+	0.470722i
$215$		0			0
$216$	1.15951	−	3.56862i	0.0788950	−	0.242814i
$217$	5.34907	+	16.4627i	0.363118	+	1.11756i
$218$	5.00395	−	3.63558i	0.338910	−	0.246232i
$219$	−14.9622			−1.01105
$220$		0			0
$221$	1.31903			0.0887276
$222$	−22.0720	+	16.0363i	−1.48138	+	1.07628i
$223$	1.33405	+	4.10580i	0.0893349	+	0.274944i	0.985736	−	0.168299i	$-0.0538276\pi$
$223$	1.33405	+	4.10580i	0.0893349	+	0.274944i	−0.896401	+	0.443244i	$0.853828\pi$
$224$	1.85335	−	5.70404i	0.123832	−	0.381117i
$225$		0			0
$226$	4.04759	+	2.94075i	0.269242	+	0.195616i
$227$	7.86025	−	24.1914i	0.521703	−	1.60564i	−0.249041	−	0.968493i	$-0.580115\pi$
$227$	7.86025	−	24.1914i	0.521703	−	1.60564i	0.770744	−	0.637145i	$-0.219885\pi$
$228$	−6.39416	−	19.6792i	−0.423464	−	1.30329i
$229$	−11.6445	+	8.46020i	−0.769488	+	0.559066i	−0.901806	−	0.432142i	$-0.857758\pi$
$229$	−11.6445	+	8.46020i	−0.769488	+	0.559066i	0.132318	+	0.991207i	$0.457758\pi$
$230$		0			0
$231$	0.697123	+	5.64256i	0.0458673	+	0.371253i
$232$	−13.1956			−0.866333
$233$	9.65280	−	7.01317i	0.632376	−	0.459448i	−0.224847	−	0.974394i	$-0.572188\pi$
$233$	9.65280	−	7.01317i	0.632376	−	0.459448i	0.857223	+	0.514946i	$0.172188\pi$
$234$	−2.58094	−	7.94332i	−0.168722	−	0.519271i
$235$		0			0
$236$	−15.5559	−	11.3020i	−1.01260	−	0.735700i
$237$	−7.11291	−	5.16783i	−0.462033	−	0.335687i
$238$	0.467435	−	1.43862i	0.0302993	−	0.0932517i
$239$	−2.55170	−	7.85333i	−0.165056	−	0.507990i	0.833985	−	0.551788i	$-0.186054\pi$
$239$	−2.55170	−	7.85333i	−0.165056	−	0.507990i	−0.999040	+	0.0437981i	$0.986054\pi$
$240$		0			0
$241$	−11.1487			−0.718154			−0.359077	−	0.933308i	$-0.616908\pi$
$241$	−11.1487			−0.718154			−0.359077	+	0.933308i	$0.616908\pi$
$242$	16.6835	−	19.9434i	1.07245	−	1.28201i
$243$	1.00000			0.0641500
$244$	9.88600	−	7.18260i	0.632886	−	0.459819i
$245$		0			0
$246$	−1.76693	+	5.43805i	−0.112655	+	0.346718i
$247$	−16.4880	−	11.9793i	−1.04911	−	0.762222i
$248$	30.6533	+	22.2709i	1.94649	+	1.41421i
$249$	2.29975	−	7.07790i	0.145741	−	0.448544i
$250$		0			0
$251$	−23.1886	+	16.8475i	−1.46365	+	1.06341i	−0.481262	+	0.876577i	$0.659822\pi$
$251$	−23.1886	+	16.8475i	−1.46365	+	1.06341i	−0.982392	+	0.186831i	$0.940178\pi$
$252$	−6.14965			−0.387392
$253$	1.54837	+	12.5326i	0.0973449	+	0.787917i
$254$	−28.2415			−1.77203
$255$		0			0
$256$	−7.81414	−	24.0494i	−0.488384	−	1.50309i
$257$	0.716932	−	2.20649i	0.0447210	−	0.137637i	−0.926203	−	0.377025i	$-0.876947\pi$
$257$	0.716932	−	2.20649i	0.0447210	−	0.137637i	0.970924	+	0.239388i	$0.0769469\pi$
$258$	0.429291	+	0.311898i	0.0267265	+	0.0194179i
$259$	16.0069	+	11.6297i	0.994619	+	0.722633i
$260$		0			0
$261$	−1.08672	−	3.34458i	−0.0672663	−	0.207024i
$262$	−38.8890	+	28.2545i	−2.40257	+	1.74557i
$263$	−2.92970			−0.180653			−0.0903265	−	0.995912i	$-0.528791\pi$
$263$	−2.92970			−0.180653			−0.0903265	+	0.995912i	$0.528791\pi$
$264$	8.49421	+	9.09522i	0.522783	+	0.559772i
$265$		0			0
$266$	−18.9083	+	13.7377i	−1.15934	+	0.842312i
$267$	4.79156	+	14.7469i	0.293239	+	0.902496i
$268$	10.0768	−	31.0131i	0.615537	−	1.89443i
$269$	3.66649	+	2.66386i	0.223550	+	0.162418i	0.693923	−	0.720049i	$-0.255881\pi$
$269$	3.66649	+	2.66386i	0.223550	+	0.162418i	−0.470373	+	0.882468i	$0.655881\pi$
$270$		0			0
$271$	8.37796	−	25.7847i	0.508925	−	1.56631i	−0.285146	−	0.958484i	$-0.592042\pi$
$271$	8.37796	−	25.7847i	0.508925	−	1.56631i	0.794071	−	0.607825i	$-0.207958\pi$
$272$	−0.195494	−	0.601670i	−0.0118536	−	0.0364816i
$273$	−4.90025	+	3.56024i	−0.296576	+	0.215475i
$274$	−12.5597			−0.758761
$275$		0			0
$276$	−13.6589			−0.822167
$277$	10.7206	−	7.78897i	0.644139	−	0.467994i	−0.217131	−	0.976142i	$-0.569670\pi$
$277$	10.7206	−	7.78897i	0.644139	−	0.467994i	0.861270	+	0.508148i	$0.169670\pi$
$278$	9.65325	+	29.7096i	0.578963	+	1.78187i
$279$	−3.12039	+	9.60356i	−0.186813	+	0.574950i
$280$		0			0
$281$	8.95715	+	6.50775i	0.534339	+	0.388220i	0.821978	−	0.569519i	$-0.192871\pi$
$281$	8.95715	+	6.50775i	0.534339	+	0.388220i	−0.287640	+	0.957739i	$0.592871\pi$
$282$	−3.41583	+	10.5128i	−0.203410	+	0.626030i
$283$	−3.11389	−	9.58356i	−0.185101	−	0.569683i	0.814849	−	0.579674i	$-0.196820\pi$
$283$	−3.11389	−	9.58356i	−0.185101	−	0.569683i	−0.999950	+	0.00999031i	$0.996820\pi$
$284$	25.4693	−	18.5045i	1.51133	−	1.09804i
$285$		0			0
$286$	27.1958	+	5.26513i	1.60812	+	0.311334i
$287$	4.14669			0.244771
$288$	2.83051	−	2.05648i	0.166789	−	0.121179i
$289$	−5.21023	−	16.0354i	−0.306484	−	0.943260i
$290$		0			0
$291$	−11.8632	−	8.61910i	−0.695431	−	0.505260i
$292$	43.4245	+	31.5498i	2.54123	+	1.84631i
$293$	−2.42473	+	7.46255i	−0.141654	+	0.435967i	−0.996566	−	0.0828074i	$-0.973611\pi$
$293$	−2.42473	+	7.46255i	−0.141654	+	0.435967i	0.854911	+	0.518774i	$0.173611\pi$
$294$	−2.96664	−	9.13037i	−0.173018	−	0.532494i
$295$		0			0
$296$	43.3085			2.51725
$297$	−1.60575	+	2.90199i	−0.0931752	+	0.168391i
$298$	−14.3312			−0.830184
$299$	−10.8838	+	7.90757i	−0.629429	+	0.457307i
$300$		0			0
$301$	0.118916	−	0.365986i	0.00685421	−	0.0210951i
$302$	14.0268	+	10.1910i	0.807150	+	0.586429i
$303$	−4.96307	−	3.60588i	−0.285121	−	0.207152i
$304$	−3.02059	+	9.29641i	−0.173242	+	0.533185i
$305$		0			0
$306$	0.713883	−	0.518666i	0.0408099	−	0.0296502i
$307$	2.64692			0.151068			0.0755339	−	0.997143i	$-0.475934\pi$
$307$	2.64692			0.151068			0.0755339	+	0.997143i	$0.475934\pi$
$308$	9.87481	−	17.8462i	0.562670	−	1.01688i
$309$	7.86989			0.447702
$310$		0			0
$311$	−1.39311	−	4.28755i	−0.0789959	−	0.243125i	0.903758	−	0.428045i	$-0.140797\pi$
$311$	−1.39311	−	4.28755i	−0.0789959	−	0.243125i	−0.982754	+	0.184920i	$0.940797\pi$
$312$	−4.09701	+	12.6093i	−0.231948	+	0.713861i
$313$	7.85494	+	5.70694i	0.443987	+	0.322576i	0.787217	−	0.616676i	$-0.211521\pi$
$313$	7.85494	+	5.70694i	0.443987	+	0.322576i	−0.343230	+	0.939251i	$0.611521\pi$
$314$	20.1862	+	14.6661i	1.13917	+	0.827656i
$315$		0			0
$316$	9.74659	+	29.9969i	0.548288	+	1.68746i
$317$	13.8145	−	10.0368i	0.775901	−	0.563725i	−0.127845	−	0.991794i	$-0.540806\pi$
$317$	13.8145	−	10.0368i	0.775901	−	0.563725i	0.903746	+	0.428069i	$0.140806\pi$
$318$	−5.77745			−0.323984
$319$	11.4509	+	2.21691i	0.641130	+	0.124123i
$320$		0			0
$321$	4.00964	−	2.91317i	0.223796	−	0.162597i
$322$	4.76750	+	14.6729i	0.265682	+	0.817687i
$323$	0.665376	−	2.04782i	0.0370225	−	0.113944i
$324$	−2.90227	−	2.10863i	−0.161237	−	0.117146i
$325$		0			0
$326$	−7.38264	+	22.7214i	−0.408887	+	1.25842i
$327$	−0.808597	−	2.48861i	−0.0447155	−	0.137620i
$328$	7.34317	−	5.33512i	0.405459	−	0.294583i
$329$	8.01638			0.441957
$330$		0			0
$331$	−2.79769			−0.153775			−0.0768874	−	0.997040i	$-0.524498\pi$
$331$	−2.79769			−0.153775			−0.0768874	+	0.997040i	$0.524498\pi$
$332$	−21.5992	+	15.6927i	−1.18541	+	0.861249i
$333$	3.56666	+	10.9770i	0.195452	+	0.601538i
$334$	−9.74940	+	30.0056i	−0.533463	+	1.64183i
$335$		0			0
$336$	2.35026	+	1.70756i	0.128217	+	0.0931551i
$337$	2.87008	−	8.83320i	0.156343	−	0.481175i	−0.841951	−	0.539554i	$-0.818593\pi$
$337$	2.87008	−	8.83320i	0.156343	−	0.481175i	0.998295	+	0.0583785i	$0.0185930\pi$
$338$	−0.376325	−	1.15821i	−0.0204694	−	0.0629984i
$339$	1.71235	−	1.24409i	0.0930019	−	0.0675698i
$340$		0			0
$341$	−22.8589	−	24.4763i	−1.23788	−	1.32546i
$342$	−13.6341			−0.737247
$343$	−15.3404	+	11.1455i	−0.828306	+	0.601799i
$344$	−0.260295	−	0.801104i	−0.0140341	−	0.0431926i
$345$		0			0
$346$	34.1548	+	24.8149i	1.83618	+	1.33406i
$347$	−7.56856	−	5.49888i	−0.406301	−	0.295195i	0.365801	−	0.930693i	$-0.380795\pi$
$347$	−7.56856	−	5.49888i	−0.406301	−	0.295195i	−0.772103	+	0.635498i	$0.780795\pi$
$348$	−3.89851	+	11.9984i	−0.208982	+	0.643180i
$349$	−0.521608	−	1.60534i	−0.0279210	−	0.0859321i	0.936125	−	0.351668i	$-0.114385\pi$
$349$	−0.521608	−	1.60534i	−0.0279210	−	0.0859321i	−0.964046	+	0.265735i	$0.914385\pi$
$350$		0			0
$351$	−3.53338			−0.188598
$352$	1.42281	+	11.5163i	0.0758359	+	0.613821i
$353$	9.60028			0.510971			0.255486	−	0.966813i	$-0.417765\pi$
$353$	9.60028			0.510971			0.255486	+	0.966813i	$0.417765\pi$
$354$	−10.2499	+	7.44700i	−0.544777	+	0.395803i
$355$		0			0
$356$	17.1893	−	52.9032i	0.911030	−	2.80386i
$357$	−0.517715	−	0.376142i	−0.0274004	−	0.0199076i
$358$	24.3577	+	17.6969i	1.28735	+	0.935312i
$359$	−8.40104	+	25.8557i	−0.443390	+	1.36461i	0.440850	+	0.897581i	$0.354677\pi$
$359$	−8.40104	+	25.8557i	−0.443390	+	1.36461i	−0.884240	+	0.467033i	$0.845323\pi$
$360$		0			0
$361$	−11.5440	+	8.38717i	−0.607576	+	0.441430i
$362$	48.9578			2.57317
$363$	−5.84312	−	9.31976i	−0.306684	−	0.489161i
$364$	21.7291			1.13891
$365$		0			0
$366$	−2.48811	−	7.65762i	−0.130056	−	0.400270i
$367$	2.38456	−	7.33892i	0.124473	−	0.383088i	−0.869332	−	0.494229i	$-0.835450\pi$
$367$	2.38456	−	7.33892i	0.124473	−	0.383088i	0.993805	+	0.111141i	$0.0354504\pi$
$368$	5.22011	+	3.79263i	0.272117	+	0.197705i
$369$	1.95699	+	1.42184i	0.101877	+	0.0740180i
$370$		0			0
$371$	1.29474	+	3.98481i	0.0672196	+	0.206881i
$372$	29.3065	−	21.2924i	1.51947	−	1.10396i
$373$	−20.0037			−1.03575			−0.517876	−	0.855456i	$-0.673277\pi$
$373$	−20.0037			−1.03575			−0.517876	+	0.855456i	$0.673277\pi$
$374$	0.358847	+	2.90453i	0.0185555	+	0.150190i
$375$		0			0
$376$	14.1958	−	10.3139i	0.732093	−	0.531896i
$377$	3.83980	+	11.8177i	0.197760	+	0.608642i
$378$	−1.25215	+	3.85373i	−0.0644038	+	0.198214i
$379$	5.43469	+	3.94854i	0.279161	+	0.202823i	0.718552	−	0.695474i	$-0.244805\pi$
$379$	5.43469	+	3.94854i	0.279161	+	0.202823i	−0.439390	+	0.898296i	$0.644805\pi$
$380$		0			0
$381$	−3.69203	+	11.3629i	−0.189148	+	0.582139i
$382$	−4.52845	−	13.9371i	−0.231695	−	0.713085i
$383$	9.18187	−	6.67102i	0.469171	−	0.340873i	−0.327947	−	0.944696i	$-0.606357\pi$
$383$	9.18187	−	6.67102i	0.469171	−	0.340873i	0.797118	+	0.603823i	$0.206357\pi$
$384$	−20.5629			−1.04935
$385$		0			0
$386$	−13.0566			−0.664562
$387$	0.181613	−	0.131949i	0.00923190	−	0.00670737i
$388$	16.2557	+	50.0300i	0.825259	+	2.53989i
$389$	−1.59639	+	4.91317i	−0.0809399	+	0.249108i	−0.983335	−	0.181802i	$-0.941807\pi$
$389$	−1.59639	+	4.91317i	−0.0809399	+	0.249108i	0.902395	+	0.430909i	$0.141807\pi$
$390$		0			0
$391$	−1.14989	−	0.835442i	−0.0581523	−	0.0422501i
$392$	−4.70926	+	14.4936i	−0.237854	+	0.732038i
$393$	6.28415	+	19.3406i	0.316993	+	0.975606i
$394$	24.5780	−	17.8569i	1.23822	−	0.899619i
$395$		0			0
$396$	10.7795	−	5.03645i	0.541693	−	0.253091i
$397$	−7.40026			−0.371408			−0.185704	−	0.982606i	$-0.559457\pi$
$397$	−7.40026			−0.371408			−0.185704	+	0.982606i	$0.559457\pi$
$398$	−6.55604	+	4.76324i	−0.328625	+	0.238760i
$399$	3.05543	+	9.40365i	0.152963	+	0.470771i
$400$		0			0
$401$	25.7212	+	18.6876i	1.28446	+	0.933213i	0.999678	−	0.0253797i	$-0.00807948\pi$
$401$	25.7212	+	18.6876i	1.28446	+	0.933213i	0.284780	+	0.958593i	$0.408079\pi$
$402$	−17.3829	−	12.6294i	−0.866978	−	0.629896i
$403$	11.0255	−	33.9331i	0.549220	−	1.69033i
$404$	6.80073	+	20.9305i	0.338349	+	1.04133i
$405$		0			0
$406$	14.2498			0.707208
$407$	−37.5825	−	7.27600i	−1.86289	−	0.360658i
$408$	−1.40074			−0.0693470
$409$	−9.62734	+	6.99467i	−0.476041	+	0.345864i	−0.799791	−	0.600279i	$-0.795056\pi$
$409$	−9.62734	+	6.99467i	−0.476041	+	0.345864i	0.323750	+	0.946143i	$0.395056\pi$
$410$		0			0
$411$	−1.64194	+	5.05338i	−0.0809910	+	0.249265i
$412$	−22.8406	−	16.5946i	−1.12527	−	0.817560i
$413$	7.43335	+	5.40064i	0.365771	+	0.265748i
$414$	−2.78113	+	8.55944i	−0.136685	+	0.420673i
$415$		0			0
$416$	−10.0013	+	7.26634i	−0.490352	+	0.356262i
$417$	13.2156			0.647169
$418$	21.8929	−	39.5660i	1.07082	−	1.93524i
$419$	6.57012			0.320971			0.160486	−	0.987038i	$-0.448694\pi$
$419$	6.57012			0.320971			0.160486	+	0.987038i	$0.448694\pi$
$420$		0			0
$421$	9.68283	+	29.8007i	0.471912	+	1.45240i	0.850077	+	0.526658i	$0.176555\pi$
$421$	9.68283	+	29.8007i	0.471912	+	1.45240i	−0.378165	+	0.925738i	$0.623445\pi$
$422$	13.0232	−	40.0814i	0.633961	−	1.95113i
$423$	3.78326	+	2.74870i	0.183948	+	0.133646i
$424$	7.41964	+	5.39068i	0.360330	+	0.261795i
$425$		0			0
$426$	−6.41012	−	19.7283i	−0.310571	−	0.955840i
$427$	−4.72399	+	3.43218i	−0.228610	+	0.166095i
$428$	−17.7799			−0.859422
$429$	5.67374	−	10.2539i	0.273931	−	0.495061i
$430$		0			0
$431$	−10.1465	+	7.37184i	−0.488738	+	0.355089i	−0.804699	−	0.593683i	$-0.797673\pi$
$431$	−10.1465	+	7.37184i	−0.488738	+	0.355089i	0.315961	+	0.948772i	$0.397673\pi$
$432$	0.523685	+	1.61174i	0.0251958	+	0.0775448i
$433$	−8.04167	+	24.7497i	−0.386458	+	1.18939i	0.548959	+	0.835849i	$0.315024\pi$
$433$	−8.04167	+	24.7497i	−0.386458	+	1.18939i	−0.935417	+	0.353546i	$0.884976\pi$
$434$	−33.1023	−	24.0502i	−1.58896	−	1.15445i
$435$		0			0
$436$	−2.90077	+	8.92764i	−0.138922	+	0.427557i
$437$	6.78636	+	20.8863i	0.324635	+	0.999125i
$438$	28.6127	−	20.7884i	1.36717	−	0.993307i
$439$	−35.0511			−1.67290			−0.836450	−	0.548044i	$-0.815373\pi$
$439$	−35.0511			−1.67290			−0.836450	+	0.548044i	$0.815373\pi$
$440$		0			0
$441$	−4.06141			−0.193400
$442$	−2.52242	+	1.83265i	−0.119979	+	0.0871701i
$443$	−8.05811	−	24.8003i	−0.382852	−	1.17830i	−0.938026	−	0.346564i	$-0.887348\pi$
$443$	−8.05811	−	24.8003i	−0.382852	−	1.17830i	0.555174	−	0.831734i	$-0.312652\pi$
$444$	12.7951	−	39.3792i	0.607227	−	1.86885i
$445$		0			0
$446$	−8.25570	−	5.99812i	−0.390919	−	0.284019i
$447$	−1.87353	+	5.76612i	−0.0886147	+	0.272728i
$448$	6.17634	+	19.0088i	0.291805	+	0.898082i
$449$	0.577580	−	0.419636i	0.0272577	−	0.0198039i	−0.574073	−	0.818804i	$-0.694637\pi$
$449$	0.577580	−	0.419636i	0.0272577	−	0.0198039i	0.601331	+	0.799000i	$0.294637\pi$
$450$		0			0
$451$	−7.26862	+	3.39606i	−0.342266	+	0.159914i
$452$	−7.59303			−0.357146
$453$	5.93407	−	4.31135i	0.278807	−	0.202565i
$454$	18.5798	+	57.1828i	0.871995	+	2.68372i
$455$		0			0
$456$	17.5094	+	12.7213i	0.819954	+	0.595732i
$457$	24.2688	+	17.6323i	1.13525	+	0.824805i	0.986450	−	0.164063i	$-0.0524601\pi$
$457$	24.2688	+	17.6323i	1.13525	+	0.824805i	0.148796	+	0.988868i	$0.452460\pi$
$458$	10.5136	−	32.3574i	0.491266	−	1.51196i
$459$	−0.115358	−	0.355034i	−0.00538443	−	0.0165716i
$460$		0			0
$461$	0.0359281			0.00167334			0.000836670	−	1.00000i	$-0.499734\pi$
$461$	0.0359281			0.00167334			0.000836670		1.00000i	$0.499734\pi$
$462$	−9.17285	−	9.82187i	−0.426759	−	0.456955i
$463$	−3.65474			−0.169850			−0.0849251	−	0.996387i	$-0.527065\pi$
$463$	−3.65474			−0.169850			−0.0849251	+	0.996387i	$0.527065\pi$
$464$	4.82149	−	3.50302i	0.223832	−	0.162623i
$465$		0			0
$466$	−8.71532	+	26.8230i	−0.403729	+	1.24255i
$467$	−12.3277	−	8.95659i	−0.570457	−	0.414462i	0.264814	−	0.964300i	$-0.414689\pi$
$467$	−12.3277	−	8.95659i	−0.570457	−	0.414462i	−0.835271	+	0.549838i	$0.814689\pi$
$468$	10.2548	+	7.45058i	0.474031	+	0.344403i
$469$	−4.81515	+	14.8195i	−0.222343	+	0.684302i
$470$		0			0
$471$	8.53981	−	6.20454i	0.393494	−	0.285890i
$472$	20.1118			0.925721
$473$	0.0912911	+	0.738917i	0.00419757	+	0.0339754i
$474$	20.7824			0.954565
$475$		0			0
$476$	0.709409	+	2.18334i	0.0325157	+	0.100073i
$477$	−0.755290	+	2.32454i	−0.0345823	+	0.106434i
$478$	15.7910	+	11.4729i	0.722265	+	0.524756i
$479$	10.1619	+	7.38305i	0.464309	+	0.337340i	0.795219	−	0.606322i	$-0.207356\pi$
$479$	10.1619	+	7.38305i	0.464309	+	0.337340i	−0.330910	+	0.943662i	$0.607356\pi$
$480$		0			0
$481$	−12.6024	−	38.7861i	−0.574619	−	1.76849i
$482$	21.3201	−	15.4899i	0.971103	−	0.705548i
$483$	6.52684			0.296982
$484$	−2.69355	+	39.3695i	−0.122434	+	1.78952i
$485$		0			0
$486$	−1.91233	+	1.38939i	−0.0867451	+	0.0630240i
$487$	0.532235	+	1.63805i	0.0241179	+	0.0742271i	0.962391	−	0.271668i	$-0.0875753\pi$
$487$	0.532235	+	1.63805i	0.0241179	+	0.0742271i	−0.938273	+	0.345895i	$0.887575\pi$
$488$	−3.94965	+	12.1558i	−0.178792	+	0.550266i
$489$	8.17677	+	5.94077i	0.369766	+	0.268651i
$490$		0			0
$491$	6.21824	−	19.1378i	0.280625	−	0.863675i	−0.707051	−	0.707163i	$-0.749975\pi$
$491$	6.21824	−	19.1378i	0.280625	−	0.863675i	0.987676	−	0.156513i	$-0.0500252\pi$
$492$	−2.68161	−	8.25314i	−0.120896	−	0.372080i
$493$	−1.06208	+	0.771645i	−0.0478336	+	0.0347532i
$494$	48.1744			2.16747
$495$		0			0
$496$	−17.1125			−0.768375
$497$	−12.1704	+	8.84233i	−0.545918	+	0.396633i
$498$	5.43608	+	16.7305i	0.243597	+	0.749713i
$499$	5.52718	−	17.0109i	0.247430	−	0.761513i	−0.747797	−	0.663928i	$-0.768888\pi$
$499$	5.52718	−	17.0109i	0.247430	−	0.761513i	0.995227	−	0.0975849i	$-0.0311117\pi$
$500$		0			0
$501$	10.7981	+	7.84529i	0.482424	+	0.350502i
$502$	20.9366	−	64.4361i	0.934444	−	2.87592i
$503$	5.06278	+	15.5816i	0.225738	+	0.694750i	0.998216	+	0.0597085i	$0.0190171\pi$
$503$	5.06278	+	15.5816i	0.225738	+	0.694750i	−0.772478	+	0.635042i	$0.780983\pi$
$504$	5.20381	−	3.78079i	0.231796	−	0.168410i
$505$		0			0
$506$	−20.3736	−	21.8152i	−0.905718	−	0.969802i
$507$	−0.515200			−0.0228808
$508$	34.6754	−	25.1931i	1.53847	−	1.11777i
$509$	0.0434607	+	0.133758i	0.00192636	+	0.00592873i	0.952015	−	0.306051i	$-0.0990079\pi$
$509$	0.0434607	+	0.133758i	0.00192636	+	0.00592873i	−0.950089	+	0.311980i	$0.899008\pi$
$510$		0			0
$511$	−20.7503	−	15.0760i	−0.917938	−	0.666921i
$512$	15.0857	+	10.9604i	0.666701	+	0.484387i
$513$	−1.78239	+	5.48564i	−0.0786945	+	0.242197i
$514$	1.69466	+	5.21564i	0.0747484	+	0.230052i
$515$		0			0
$516$	−0.805322			−0.0354523
$517$	−14.0517	+	6.56526i	−0.617992	+	0.288740i
$518$	−46.7686			−2.05489
$519$	14.4493	−	10.4980i	0.634254	−	0.460813i
$520$		0			0
$521$	1.82811	−	5.62634i	0.0800909	−	0.246495i	−0.902991	−	0.429659i	$-0.858634\pi$
$521$	1.82811	−	5.62634i	0.0800909	−	0.246495i	0.983082	+	0.183164i	$0.0586339\pi$
$522$	6.72509	+	4.88606i	0.294349	+	0.213857i
$523$	15.3518	+	11.1538i	0.671289	+	0.487720i	0.870456	−	0.492246i	$-0.163824\pi$
$523$	15.3518	+	11.1538i	0.671289	+	0.487720i	−0.199168	+	0.979965i	$0.563824\pi$
$524$	22.5438	−	69.3827i	0.984831	−	3.03100i
$525$		0			0
$526$	5.60255	−	4.07049i	0.244283	−	0.177482i
$527$	3.76955			0.164204
$528$	−5.51816	−	1.06832i	−0.240147	−	0.0464927i
$529$	−8.50336			−0.369711
$530$		0			0
$531$	1.65630	+	5.09757i	0.0718774	+	0.221216i
$532$	10.9611	−	33.7347i	0.475223	−	1.46259i
$533$	−6.91481	−	5.02391i	−0.299514	−	0.217610i
$534$	−29.6522	−	21.5436i	−1.28318	−	0.932283i
$535$		0			0
$536$	10.5398	+	32.4383i	0.455252	+	1.40112i
$537$	10.3046	−	7.48674i	0.444677	−	0.323077i
$538$	−10.7127			−0.461856
$539$	6.52162	−	11.7862i	0.280906	−	0.507667i
$540$		0			0
$541$	−14.8245	+	10.7706i	−0.637354	+	0.463065i	−0.858940	−	0.512076i	$-0.828877\pi$
$541$	−14.8245	+	10.7706i	−0.637354	+	0.463065i	0.221586	+	0.975141i	$0.428877\pi$
$542$	19.8036	+	60.9491i	0.850636	+	2.61799i
$543$	6.40028	−	19.6980i	0.274662	−	0.845324i
$544$	−1.05664	−	0.767696i	−0.0453032	−	0.0329147i
$545$		0			0
$546$	4.42433	−	13.6167i	0.189344	−	0.582741i
$547$	9.53561	+	29.3476i	0.407713	+	1.25481i	0.918608	+	0.395169i	$0.129314\pi$
$547$	9.53561	+	29.3476i	0.407713	+	1.25481i	−0.510895	+	0.859643i	$0.670686\pi$
$548$	15.4210	−	11.2040i	0.658754	−	0.478613i
$549$	−3.40629			−0.145377
$550$		0			0
$551$	20.2841			0.864132
$552$	11.5581	−	8.39743i	0.491944	−	0.357418i
$553$	−4.65738	−	14.3339i	−0.198052	−	0.609541i
$554$	−9.67942	+	29.7902i	−0.411239	+	1.26566i
$555$		0			0
$556$	−38.3552	−	27.8667i	−1.62662	−	1.18181i
$557$	−11.5221	+	35.4614i	−0.488207	+	1.50255i	0.339075	+	0.940759i	$0.389886\pi$
$557$	−11.5221	+	35.4614i	−0.488207	+	1.50255i	−0.827282	+	0.561787i	$0.810114\pi$
$558$	−7.37587	−	22.7006i	−0.312246	−	0.960993i
$559$	−0.641708	+	0.466228i	−0.0271413	+	0.0197193i
$560$		0			0
$561$	1.21554	+	0.235330i	0.0513202	+	0.00993564i
$562$	−26.1708			−1.10395
$563$	−14.9463	+	10.8591i	−0.629912	+	0.457658i	−0.856370	−	0.516363i	$-0.827285\pi$
$563$	−14.9463	+	10.8591i	−0.629912	+	0.457658i	0.226458	+	0.974021i	$0.427285\pi$
$564$	−5.18408	−	15.9550i	−0.218289	−	0.671825i
$565$		0			0
$566$	19.2701	+	14.0005i	0.809981	+	0.588486i
$567$	1.38684	+	1.00760i	0.0582419	+	0.0423152i
$568$	−10.1755	+	31.3169i	−0.426954	+	1.31403i
$569$	−12.9706	−	39.9193i	−0.543755	−	1.67351i	−0.723932	−	0.689872i	$-0.757667\pi$
$569$	−12.9706	−	39.9193i	−0.543755	−	1.67351i	0.180176	−	0.983634i	$-0.442333\pi$
$570$		0			0
$571$	−9.70741			−0.406243			−0.203121	−	0.979154i	$-0.565109\pi$
$571$	−9.70741			−0.406243			−0.203121	+	0.979154i	$0.565109\pi$
$572$	−38.0883	+	17.7957i	−1.59255	+	0.744076i
$573$	−6.19957			−0.258991
$574$	−7.92984	+	5.76137i	−0.330985	+	0.240475i
$575$		0			0
$576$	−3.60298	+	11.0888i	−0.150124	+	0.462034i
$577$	−10.5420	−	7.65924i	−0.438871	−	0.318859i	0.346315	−	0.938118i	$-0.387433\pi$
$577$	−10.5420	−	7.65924i	−0.438871	−	0.318859i	−0.785186	+	0.619260i	$0.787433\pi$
$578$	32.2431	+	23.4260i	1.34114	+	0.974393i
$579$	−1.70689	+	5.25328i	−0.0709361	+	0.218319i
$580$		0			0
$581$	10.3211	−	7.49871i	0.428191	−	0.311099i
$582$	34.6616			1.43677
$583$	−5.53300	−	5.92448i	−0.229153	−	0.245367i
$584$	−56.1423			−2.32319
$585$		0			0
$586$	−5.73150	−	17.6397i	−0.236766	−	0.728691i
$587$	−13.3614	+	41.1222i	−0.551485	+	1.69730i	0.153565	+	0.988139i	$0.450925\pi$
$587$	−13.3614	+	41.1222i	−0.551485	+	1.69730i	−0.705050	+	0.709158i	$0.749075\pi$
$588$	11.7873	+	8.56399i	0.486101	+	0.353173i
$589$	−47.1199	−	34.2346i	−1.94154	−	1.41061i
$590$		0			0
$591$	−3.97160	−	12.2233i	−0.163370	−	0.502800i
$592$	−15.8243	+	11.4970i	−0.650375	+	0.472525i
$593$	34.9632			1.43576			0.717882	−	0.696164i	$-0.245112\pi$
$593$	34.9632			1.43576			0.717882	+	0.696164i	$0.245112\pi$
$594$	−0.961269	−	7.78058i	−0.0394414	−	0.319241i
$595$		0			0
$596$	17.5961	−	12.7843i	0.720763	−	0.523665i
$597$	1.05940	+	3.26051i	0.0433585	+	0.133444i
$598$	9.82680	−	30.2438i	0.401848	−	1.23676i
$599$	−18.2378	−	13.2505i	−0.745174	−	0.541401i	0.149153	−	0.988814i	$-0.452345\pi$
$599$	−18.2378	−	13.2505i	−0.745174	−	0.541401i	−0.894327	+	0.447413i	$0.852345\pi$
$600$		0			0
$601$	−6.16194	+	18.9645i	−0.251351	+	0.773578i	0.743176	+	0.669096i	$0.233318\pi$
$601$	−6.16194	+	18.9645i	−0.251351	+	0.773578i	−0.994527	+	0.104482i	$0.966682\pi$
$602$	0.281090	+	0.865107i	0.0114564	+	0.0352591i
$603$	−7.35387	+	5.34290i	−0.299473	+	0.217580i
$604$	−26.3133			−1.07067
$605$		0			0
$606$	14.5010			0.589063
$607$	−13.2747	+	9.64463i	−0.538803	+	0.391463i	−0.823640	−	0.567113i	$-0.808060\pi$
$607$	−13.2747	+	9.64463i	−0.538803	+	0.391463i	0.284837	+	0.958576i	$0.408060\pi$
$608$	6.23605	+	19.1926i	0.252905	+	0.778362i
$609$	1.86289	−	5.73338i	0.0754881	−	0.232328i
$610$		0			0
$611$	−13.3677	−	9.71221i	−0.540800	−	0.392914i
$612$	−0.413835	+	1.27365i	−0.0167283	+	0.0514844i
$613$	11.5202	+	35.4555i	0.465297	+	1.43204i	0.858609	+	0.512631i	$0.171329\pi$
$613$	11.5202	+	35.4555i	0.465297	+	1.43204i	−0.393313	+	0.919405i	$0.628671\pi$
$614$	−5.06179	+	3.67761i	−0.204277	+	0.148416i
$615$		0			0
$616$	2.61579	+	21.1724i	0.105393	+	0.853061i
$617$	−28.7965			−1.15930			−0.579651	−	0.814865i	$-0.696811\pi$
$617$	−28.7965			−1.15930			−0.579651	+	0.814865i	$0.696811\pi$
$618$	−15.0498	+	10.9343i	−0.605393	+	0.439844i
$619$	2.58639	+	7.96009i	0.103956	+	0.319943i	0.989484	−	0.144643i	$-0.0462032\pi$
$619$	2.58639	+	7.96009i	0.103956	+	0.319943i	−0.885528	+	0.464586i	$0.846203\pi$
$620$		0			0
$621$	3.08029	+	2.23796i	0.123608	+	0.0898062i
$622$	8.62116	+	6.26364i	0.345677	+	0.251149i
$623$	−8.21384	+	25.2796i	−0.329081	+	1.01281i
$624$	−1.85038	−	5.69489i	−0.0740746	−	0.227978i
$625$		0			0
$626$	−22.9504			−0.917282
$627$	−13.0572	−	13.9811i	−0.521454	−	0.558350i
$628$	−37.8679			−1.51109
$629$	3.48579	−	2.53257i	0.138987	−	0.100980i
$630$		0			0
$631$	−9.24911	+	28.4658i	−0.368201	+	1.13321i	0.579751	+	0.814794i	$0.303150\pi$
$631$	−9.24911	+	28.4658i	−0.368201	+	1.13321i	−0.947952	+	0.318413i	$0.896850\pi$
$632$	−26.6895	−	19.3911i	−1.06165	−	0.771336i
$633$	−14.4241	−	10.4797i	−0.573307	−	0.416532i
$634$	−12.4729	+	38.3875i	−0.495360	+	1.52456i
$635$		0			0
$636$	7.09365	−	5.15384i	0.281281	−	0.204363i
$637$	14.3505			0.568588
$638$	−24.9781	+	11.6704i	−0.988894	+	0.462034i
$639$	−8.77564			−0.347159
$640$		0			0
$641$	0.654461	+	2.01423i	0.0258497	+	0.0795571i	0.963149	−	0.268968i	$-0.0866826\pi$
$641$	0.654461	+	2.01423i	0.0258497	+	0.0795571i	−0.937299	+	0.348525i	$0.886683\pi$
$642$	−3.62022	+	11.1419i	−0.142879	+	0.439735i
$643$	−15.6415	−	11.3642i	−0.616841	−	0.448161i	0.234976	−	0.972001i	$-0.424499\pi$
$643$	−15.6415	−	11.3642i	−0.616841	−	0.448161i	−0.851817	+	0.523840i	$0.824499\pi$
$644$	−18.9427	−	13.7627i	−0.746447	−	0.542325i
$645$		0			0
$646$	1.57279	+	4.84056i	0.0618808	+	0.190449i
$647$	1.70192	−	1.23652i	0.0669094	−	0.0486125i	−0.553828	−	0.832631i	$-0.686833\pi$
$647$	1.70192	−	1.23652i	0.0669094	−	0.0486125i	0.620737	+	0.784019i	$0.286833\pi$
$648$	3.75227			0.147403
$649$	−17.4527	−	3.37886i	−0.685080	−	0.132632i
$650$		0			0
$651$	−14.0040	+	10.1745i	−0.548861	+	0.398771i
$652$	−11.2044	−	34.4835i	−0.438797	−	1.35048i
$653$	0.810347	−	2.49399i	0.0317113	−	0.0975974i	−0.933948	−	0.357409i	$-0.883660\pi$
$653$	0.810347	−	2.49399i	0.0317113	−	0.0975974i	0.965659	+	0.259811i	$0.0836603\pi$
$654$	5.00395	+	3.63558i	0.195670	+	0.142162i
$655$		0			0
$656$	−1.26678	+	3.89876i	−0.0494596	+	0.152221i
$657$	−4.62358	−	14.2299i	−0.180383	−	0.555162i
$658$	−15.3300	+	11.1379i	−0.597624	+	0.434199i
$659$	36.2473			1.41199			0.705997	−	0.708215i	$-0.250499\pi$
$659$	36.2473			1.41199			0.705997	+	0.708215i	$0.250499\pi$
$660$		0			0
$661$	22.6488			0.880937			0.440469	−	0.897768i	$-0.354812\pi$
$661$	22.6488			0.880937			0.440469	+	0.897768i	$0.354812\pi$
$662$	5.35010	−	3.88707i	0.207938	−	0.151075i
$663$	0.407603	+	1.25447i	0.0158300	+	0.0487197i
$664$	8.62928	−	26.5582i	0.334881	−	1.03066i
$665$		0			0
$666$	−22.0720	−	16.0363i	−0.855273	−	0.621392i
$667$	4.13763	−	12.7343i	0.160210	−	0.493074i
$668$	−14.7963	−	45.5384i	−0.572486	−	1.76193i
$669$	−3.49260	+	2.53752i	−0.135032	+	0.0981063i
$670$		0			0
$671$	5.46966	−	9.88504i	0.211154	−	0.381608i
$672$	5.99758			0.231362
$673$	29.9438	−	21.7554i	1.15425	−	0.838610i	0.165208	−	0.986259i	$-0.447171\pi$
$673$	29.9438	−	21.7554i	1.15425	−	0.838610i	0.989040	+	0.147649i	$0.0471705\pi$
$674$	6.78421	+	20.8797i	0.261318	+	0.804254i
$675$		0			0
$676$	1.49525	+	1.08636i	0.0575097	+	0.0417832i
$677$	24.0410	+	17.4668i	0.923969	+	0.671303i	0.944509	−	0.328486i	$-0.106538\pi$
$677$	24.0410	+	17.4668i	0.923969	+	0.671303i	−0.0205398	+	0.999789i	$0.506538\pi$
$678$	−1.54604	+	4.75823i	−0.0593754	+	0.182739i
$679$	−7.76775	−	23.9067i	−0.298099	−	0.917454i
$680$		0			0
$681$	25.4363			0.974722
$682$	77.7208	+	15.0468i	2.97608	+	0.576172i
$683$	2.06173			0.0788899			0.0394450	−	0.999222i	$-0.487441\pi$
$683$	2.06173			0.0788899			0.0394450	+	0.999222i	$0.487441\pi$
$684$	16.7401	−	12.1624i	0.640075	−	0.465042i
$685$		0			0
$686$	13.8506	−	42.6277i	0.528817	−	1.62753i
$687$	−11.6445	−	8.46020i	−0.444264	−	0.322777i
$688$	0.307776	+	0.223612i	0.0117338	+	0.00852514i
$689$	2.66873	−	8.21350i	0.101670	−	0.312910i
$690$		0			0
$691$	−2.40744	+	1.74910i	−0.0915832	+	0.0665391i	−0.632635	−	0.774450i	$-0.718026\pi$
$691$	−2.40744	+	1.74910i	−0.0915832	+	0.0665391i	0.541051	+	0.840990i	$0.318026\pi$
$692$	−64.0723			−2.43566
$693$	−5.15097	+	2.40665i	−0.195669	+	0.0914211i
$694$	22.1137			0.839423
$695$		0			0
$696$	−4.07766	−	12.5498i	−0.154563	−	0.475697i
$697$	0.279048	−	0.858820i	0.0105697	−	0.0325301i
$698$	3.22793	+	2.34523i	0.122179	+	0.0887683i
$699$	9.65280	+	7.01317i	0.365102	+	0.265262i
$700$		0			0
$701$	13.1671	+	40.5240i	0.497313	+	1.53057i	0.813321	+	0.581815i	$0.197657\pi$
$701$	13.1671	+	40.5240i	0.497313	+	1.53057i	−0.316008	+	0.948756i	$0.602343\pi$
$702$	6.75700	−	4.90924i	0.255026	−	0.185288i
$703$	−66.5733			−2.51086
$704$	−26.3942	−	28.2617i	−0.994769	−	1.06515i
$705$		0			0
$706$	−18.3589	+	13.3385i	−0.690946	+	0.502002i
$707$	−3.24971	−	10.0016i	−0.122218	−	0.376148i
$708$	5.94183	−	18.2871i	0.223308	−	0.687271i
$709$	33.6641	+	24.4584i	1.26428	+	0.918555i	0.998960	−	0.0456046i	$-0.0145214\pi$
$709$	33.6641	+	24.4584i	1.26428	+	0.918555i	0.265323	+	0.964160i	$0.414521\pi$
$710$		0			0
$711$	2.71689	−	8.36172i	0.101891	−	0.313589i
$712$	17.9792	+	55.3343i	0.673800	+	2.07374i
$713$	−31.1041	+	22.5984i	−1.16486	+	0.846318i
$714$	1.51265			0.0566095
$715$		0			0
$716$	−45.6936			−1.70765
$717$	6.68044	−	4.85363i	0.249486	−	0.181262i
$718$	−19.8581	−	61.1170i	−0.741098	−	2.28087i
$719$	1.51504	−	4.66282i	0.0565015	−	0.173894i	−0.918823	−	0.394670i	$-0.870859\pi$
$719$	1.51504	−	4.66282i	0.0565015	−	0.173894i	0.975325	+	0.220776i	$0.0708590\pi$
$720$		0			0
$721$	10.9143	+	7.92970i	0.406470	+	0.295317i
$722$	10.4228	−	32.0781i	0.387897	−	1.19382i
$723$	−3.44515	−	10.6031i	−0.128127	−	0.394333i
$724$	−60.1112	+	43.6733i	−2.23401	+	1.62311i
$725$		0			0
$726$	24.1228	+	9.70409i	0.895279	+	0.360153i
$727$	−9.26283			−0.343539			−0.171770	−	0.985137i	$-0.554948\pi$
$727$	−9.26283			−0.343539			−0.171770	+	0.985137i	$0.554948\pi$
$728$	−18.3870	+	13.3590i	−0.681469	+	0.495116i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	−0.0677970	−	0.0492574i	−0.00250756	−	0.00182185i
$732$	9.88600	+	7.18260i	0.365397	+	0.265477i
$733$	4.21886	−	12.9843i	0.155827	−	0.479587i	−0.842416	−	0.538827i	$-0.818868\pi$
$733$	4.21886	−	12.9843i	0.155827	−	0.479587i	0.998244	+	0.0592398i	$0.0188677\pi$
$734$	5.63655	+	17.3475i	0.208049	+	0.640308i
$735$		0			0
$736$	13.3211			0.491022
$737$	−3.69656	−	29.9202i	−0.136165	−	1.10213i
$738$	−5.71791			−0.210479
$739$	35.7048	−	25.9410i	1.31342	−	0.954256i	0.313432	−	0.949611i	$-0.398521\pi$
$739$	35.7048	−	25.9410i	1.31342	−	0.954256i	0.999989	−	0.00464584i	$-0.00147882\pi$
$740$		0			0
$741$	6.29787	−	19.3829i	0.231358	−	0.712047i
$742$	−8.01242	−	5.82136i	−0.294145	−	0.213709i
$743$	−12.0136	−	8.72840i	−0.440737	−	0.320214i	0.345191	−	0.938532i	$-0.387814\pi$
$743$	−12.0136	−	8.72840i	−0.440737	−	0.320214i	−0.785928	+	0.618319i	$0.787814\pi$
$744$	−11.7085	+	36.0351i	−0.429255	+	1.32111i
$745$		0			0
$746$	38.2537	−	27.7929i	1.40057	−	1.01757i
$747$	7.44215			0.272294
$748$	−3.03161	−	3.24612i	−0.110847	−	0.118690i
$749$	8.49605			0.310439
$750$		0			0
$751$	−1.17408	−	3.61343i	−0.0428426	−	0.131856i	0.927347	−	0.374202i	$-0.122083\pi$
$751$	−1.17408	−	3.61343i	−0.0428426	−	0.131856i	−0.970190	+	0.242346i	$0.922083\pi$
$752$	−2.44894	+	7.53708i	−0.0893038	+	0.274849i
$753$	−23.1886	−	16.8475i	−0.845041	−	0.613958i
$754$	−23.7623	−	17.2643i	−0.865373	−	0.628730i
$755$		0			0
$756$	−1.90035	−	5.84866i	−0.0691149	−	0.212714i
$757$	−5.75954	+	4.18455i	−0.209334	+	0.152090i	−0.687512	−	0.726173i	$-0.741297\pi$
$757$	−5.75954	+	4.18455i	−0.209334	+	0.152090i	0.478178	+	0.878263i	$0.341297\pi$
$758$	−15.8790			−0.576751
$759$	−11.4407	+	5.34536i	−0.415272	+	0.194024i
$760$		0			0
$761$	−4.43096	+	3.21928i	−0.160622	+	0.116699i	−0.665193	−	0.746671i	$-0.731651\pi$
$761$	−4.43096	+	3.21928i	−0.160622	+	0.116699i	0.504571	+	0.863370i	$0.331651\pi$
$762$	−8.72711	−	26.8593i	−0.316150	−	0.973009i
$763$	1.38612	−	4.26605i	0.0501810	−	0.154441i
$764$	17.9929	+	13.0726i	0.650959	+	0.472949i
$765$		0			0
$766$	−8.29012	+	25.5144i	−0.299534	+	0.921872i
$767$	−5.85235	−	18.0117i	−0.211316	−	0.650364i
$768$	20.4577	−	14.8634i	0.738203	−	0.536336i
$769$	40.9023			1.47498			0.737488	−	0.675360i	$-0.236012\pi$
$769$	40.9023			1.47498			0.737488	+	0.675360i	$0.236012\pi$
$770$		0			0
$771$	2.32004			0.0835542
$772$	16.0311	−	11.6473i	0.576971	−	0.419194i
$773$	8.73179	+	26.8737i	0.314061	+	0.966579i	0.976139	+	0.217145i	$0.0696744\pi$
$773$	8.73179	+	26.8737i	0.314061	+	0.966579i	−0.662079	+	0.749434i	$0.730326\pi$
$774$	−0.163975	+	0.504662i	−0.00589394	+	0.0181397i
$775$		0			0
$776$	−44.5138	−	32.3412i	−1.59795	−	1.16098i
$777$	−6.11408	+	18.8172i	−0.219341	+	0.675063i
$778$	−3.77349	−	11.6136i	−0.135286	−	0.416368i
$779$	−11.2878	+	8.20108i	−0.404428	+	0.293834i
$780$		0			0
$781$	14.0915	−	25.4668i	0.504233	−	0.911275i
$782$	3.35972			0.120143
$783$	2.84507	−	2.06706i	0.101674	−	0.0738708i
$784$	−2.12690	−	6.54593i	−0.0759607	−	0.233783i
$785$		0			0
$786$	−38.8890	−	28.2545i	−1.38713	−	1.00781i
$787$	−10.4835	−	7.61672i	−0.373697	−	0.271507i	0.385045	−	0.922898i	$-0.374186\pi$
$787$	−10.4835	−	7.61672i	−0.373697	−	0.271507i	−0.758742	+	0.651391i	$0.774186\pi$
$788$	−14.2477	+	43.8500i	−0.507555	+	1.56209i
$789$	−0.905327	−	2.78631i	−0.0322305	−	0.0991952i
$790$		0			0
$791$	3.62830			0.129008
$792$	−6.02521	+	10.8891i	−0.214097	+	0.386926i
$793$	12.0357			0.427402
$794$	14.1517	−	10.2818i	0.502227	−	0.364889i
$795$		0			0
$796$	3.80051	−	11.6968i	0.134706	−	0.414581i
$797$	20.4441	+	14.8535i	0.724167	+	0.526138i	0.887713	−	0.460397i	$-0.152293\pi$
$797$	20.4441	+	14.8535i	0.724167	+	0.526138i	−0.163546	+	0.986536i	$0.552293\pi$
$798$	−18.9083	−	13.7377i	−0.669347	−	0.486309i
$799$	0.539454	−	1.66027i	0.0190845	−	0.0587361i
$800$		0			0
$801$	−12.5445	+	9.11409i	−0.443237	+	0.322030i
$802$	−75.1518			−2.65370
$803$	48.7195	+	9.43213i	1.71927	+	0.332853i
$804$	32.6091			1.15003
$805$		0			0
$806$	26.0618	+	80.2100i	0.917988	+	2.82528i
$807$	−1.40047	+	4.31022i	−0.0492990	+	0.151727i
$808$	−18.6228	−	13.5302i	−0.655146	−	0.475992i
$809$	−22.2093	−	16.1360i	−0.780837	−	0.567311i	0.124393	−	0.992233i	$-0.460302\pi$
$809$	−22.2093	−	16.1360i	−0.780837	−	0.567311i	−0.905230	+	0.424922i	$0.860302\pi$
$810$		0			0
$811$	−11.0813	−	34.1048i	−0.389117	−	1.19758i	−0.933449	−	0.358710i	$-0.883217\pi$
$811$	−11.0813	−	34.1048i	−0.389117	−	1.19758i	0.544331	−	0.838870i	$-0.316783\pi$
$812$	−17.4962	+	12.7117i	−0.613996	+	0.446094i
$813$	27.1116			0.950847
$814$	81.9793	−	38.3026i	2.87337	−	1.34250i
$815$		0			0
$816$	0.511811	−	0.371853i	0.0179170	−	0.0130174i
$817$	0.400121	+	1.23145i	0.0139985	+	0.0430829i
$818$	8.69233	−	26.7522i	0.303920	−	0.935370i
$819$	−4.90025	−	3.56024i	−0.171229	−	0.124405i
$820$		0			0
$821$	16.7522	−	51.5579i	0.584655	−	1.79938i	−0.0159955	−	0.999872i	$-0.505092\pi$
$821$	16.7522	−	51.5579i	0.584655	−	1.79938i	0.600651	−	0.799512i	$-0.294908\pi$
$822$	−3.88117	−	11.9450i	−0.135371	−	0.416630i
$823$	3.84331	−	2.79233i	0.133969	−	0.0973344i	−0.518782	−	0.854906i	$-0.673615\pi$
$823$	3.84331	−	2.79233i	0.133969	−	0.0973344i	0.652752	+	0.757572i	$0.273615\pi$
$824$	29.5299			1.02872
$825$		0			0
$826$	−21.7186			−0.755687
$827$	28.0434	−	20.3747i	0.975165	−	0.708499i	0.0185425	−	0.999828i	$-0.494097\pi$
$827$	28.0434	−	20.3747i	0.975165	−	0.708499i	0.956623	+	0.291329i	$0.0940974\pi$
$828$	−4.22082	−	12.9903i	−0.146684	−	0.451446i
$829$	−5.49342	+	16.9070i	−0.190794	+	0.587205i	−1.00000		0.000320867i	$-0.999898\pi$
$829$	−5.49342	+	16.9070i	−0.190794	+	0.587205i	0.809206	+	0.587526i	$0.199898\pi$
$830$		0			0
$831$	10.7206	+	7.78897i	0.371894	+	0.270197i
$832$	12.7307	−	39.1811i	0.441358	−	1.35836i
$833$	0.468514	+	1.44194i	0.0162331	+	0.0499602i
$834$	−25.2725	+	18.3616i	−0.875116	+	0.635809i
$835$		0			0
$836$	8.41475	+	68.1096i	0.291030	+	2.35562i
$837$	−10.0978			−0.349030
$838$	−12.5642	+	9.12845i	−0.434024	+	0.315337i
$839$	12.8972	+	39.6936i	0.445262	+	1.37038i	0.882196	+	0.470882i	$0.156064\pi$
$839$	12.8972	+	39.6936i	0.445262	+	1.37038i	−0.436934	+	0.899493i	$0.643936\pi$
$840$		0			0
$841$	13.4562	+	9.77653i	0.464008	+	0.337122i
$842$	−59.9215	−	43.5355i	−2.06503	−	1.50033i
$843$	−3.42133	+	10.5298i	−0.117837	+	0.362664i
$844$	19.7649	+	60.8301i	0.680336	+	2.09386i
$845$		0			0
$846$	−11.0539			−0.380039
$847$	1.28710	−	18.8126i	0.0442254	−	0.646408i
$848$	−4.14209			−0.142240
$849$	8.15226	−	5.92296i	0.279785	−	0.203276i
$850$		0			0
$851$	−13.5799	+	41.7945i	−0.465512	+	1.43270i
$852$	25.4693	+	18.5045i	0.872564	+	0.633955i
$853$	30.2327	+	21.9653i	1.03515	+	0.752079i	0.969332	−	0.245753i	$-0.0790352\pi$
$853$	30.2327	+	21.9653i	1.03515	+	0.752079i	0.0658151	+	0.997832i	$0.479035\pi$
$854$	4.26520	−	13.1269i	0.145952	−	0.449194i
$855$		0			0
$856$	15.0452	−	10.9310i	0.514236	−	0.373614i
$857$	−14.6046			−0.498884			−0.249442	−	0.968390i	$-0.580247\pi$
$857$	−14.6046			−0.498884			−0.249442	+	0.968390i	$0.580247\pi$
$858$	3.39653	+	27.4918i	0.115956	+	0.938554i
$859$	−2.27238			−0.0775325			−0.0387663	−	0.999248i	$-0.512343\pi$
$859$	−2.27238			−0.0775325			−0.0387663	+	0.999248i	$0.512343\pi$
$860$		0			0
$861$	1.28140	+	3.94374i	0.0436699	+	0.134402i
$862$	9.16104	−	28.1948i	0.312026	−	0.960318i
$863$	−40.1913	−	29.2007i	−1.36813	−	0.994002i	−0.997881	−	0.0650685i	$-0.979273\pi$
$863$	−40.1913	−	29.2007i	−1.36813	−	0.994002i	−0.370246	−	0.928934i	$-0.620727\pi$
$864$	2.83051	+	2.05648i	0.0962958	+	0.0699630i
$865$		0			0
$866$	−19.0087	−	58.5026i	−0.645940	−	1.98800i
$867$	13.6405	−	9.91044i	0.463257	−	0.336576i
$868$	62.0978			2.10774
$869$	19.9030	+	21.3112i	0.675163	+	0.722934i
$870$		0			0
$871$	25.9840	−	18.8785i	0.880435	−	0.639674i
$872$	−3.03407	−	9.33791i	−0.102747	−	0.316222i
$873$	4.53133	−	13.9460i	0.153362	−	0.472000i
$874$	−41.9969	−	30.5125i	−1.42057	−	1.03210i
$875$		0			0
$876$	−16.5867	+	51.0486i	−0.560412	+	1.72477i
$877$	−3.20671	−	9.86924i	−0.108283	−	0.333261i	0.882204	−	0.470867i	$-0.156059\pi$
$877$	−3.20671	−	9.86924i	−0.108283	−	0.333261i	−0.990487	+	0.137607i	$0.956059\pi$
$878$	67.0293	−	48.6997i	2.26213	−	1.64353i
$879$	−7.84659			−0.264659
$880$		0			0
$881$	38.5784			1.29974			0.649869	−	0.760046i	$-0.274824\pi$
$881$	38.5784			1.29974			0.649869	+	0.760046i	$0.274824\pi$
$882$	7.76675	−	5.64288i	0.261520	−	0.190006i
$883$	−5.51877	−	16.9850i	−0.185721	−	0.571591i	0.814239	−	0.580530i	$-0.197155\pi$
$883$	−5.51877	−	16.9850i	−0.185721	−	0.571591i	−0.999960	+	0.00893886i	$0.997155\pi$
$884$	1.46224	−	4.50030i	0.0491804	−	0.151362i
$885$		0			0
$886$	49.8671	+	36.2305i	1.67532	+	1.21719i
$887$	−12.5705	+	38.6881i	−0.422077	+	1.29902i	0.483689	+	0.875240i	$0.339297\pi$
$887$	−12.5705	+	38.6881i	−0.422077	+	1.29902i	−0.905766	+	0.423779i	$0.860703\pi$
$888$	13.3831	+	41.1888i	0.449106	+	1.38221i
$889$	−16.5695	+	12.0385i	−0.555724	+	0.403757i
$890$		0			0
$891$	−3.25616	−	0.630396i	−0.109086	−	0.0211191i
$892$	15.4872			0.518549
$893$	−21.8216	+	15.8543i	−0.730232	+	0.530545i
$894$	−4.42858	−	13.6298i	−0.148114	−	0.455848i
$895$		0			0
$896$	−28.5176	−	20.7192i	−0.952705	−	0.692180i
$897$	−10.8838	−	7.90757i	−0.363401	−	0.264026i
$898$	−0.521485	+	1.60497i	−0.0174022	+	0.0535584i
$899$	10.9735	+	33.7728i	0.365985	+	1.12639i
$900$		0			0
$901$	0.912421			0.0303971
$902$	9.18154	−	16.5933i	0.305712	−	0.552497i
$903$	0.384821			0.0128060
$904$	6.42518	−	4.66817i	0.213698	−	0.155261i
$905$		0			0
$906$	−5.35775	+	16.4895i	−0.177999	+	0.547826i
$907$	13.9924	+	10.1661i	0.464610	+	0.337559i	0.795337	−	0.606168i	$-0.207294\pi$
$907$	13.9924	+	10.1661i	0.464610	+	0.337559i	−0.330727	+	0.943726i	$0.607294\pi$
$908$	−73.8232	−	53.6357i	−2.44991	−	1.77996i
$909$	1.89572	−	5.83444i	0.0628772	−	0.193516i
$910$		0			0
$911$	−37.8876	+	27.5270i	−1.25527	+	0.912009i	−0.998516	−	0.0544664i	$-0.982654\pi$
$911$	−37.8876	+	27.5270i	−1.25527	+	0.912009i	−0.256758	+	0.966476i	$0.582654\pi$
$912$	−9.77482			−0.323677
$913$	−11.9502	+	21.5971i	−0.395495	+	0.714758i
$914$	−70.9081			−2.34543
$915$		0			0
$916$	15.9560	+	49.1076i	0.527202	+	1.62256i
$917$	−10.7725	+	33.1543i	−0.355739	+	1.09485i
$918$	0.713883	+	0.518666i	0.0235616	+	0.0171185i
$919$	34.1795	+	24.8329i	1.12748	+	0.819161i	0.985326	−	0.170684i	$-0.0545978\pi$
$919$	34.1795	+	24.8329i	1.12748	+	0.819161i	0.142152	+	0.989845i	$0.454598\pi$
$920$		0			0
$921$	0.817944	+	2.51737i	0.0269522	+	0.0829503i
$922$	−0.0687064	+	0.0499181i	−0.00226273	+	0.00164397i
$923$	31.0077			1.02063
$924$	20.0243	+	3.87671i	0.658750	+	0.127535i
$925$		0			0
$926$	6.98907	−	5.07786i	0.229675	−	0.166869i
$927$	2.43193	+	7.48471i	0.0798750	+	0.245830i
$928$	3.80210	−	11.7017i	0.124810	−	0.384126i
$929$	−9.24843	−	6.71938i	−0.303431	−	0.220456i	0.425642	−	0.904892i	$-0.360048\pi$
$929$	−9.24843	−	6.71938i	−0.303431	−	0.220456i	−0.729073	+	0.684436i	$0.760048\pi$
$930$		0			0
$931$	7.23902	−	22.2794i	0.237249	−	0.730178i
$932$	−13.2269	−	40.7083i	−0.433262	−	1.33344i
$933$	3.64721	−	2.64985i	0.119404	−	0.0867522i
$934$	36.0188			1.17857
$935$		0			0
$936$	−13.2582			−0.433358
$937$	1.18689	−	0.862330i	0.0387742	−	0.0281711i	−0.568229	−	0.822870i	$-0.692371\pi$
$937$	1.18689	−	0.862330i	0.0387742	−	0.0281711i	0.607004	+	0.794699i	$0.292371\pi$
$938$	−11.3819	−	35.0299i	−0.371633	−	1.14377i
$939$	−3.00032	+	9.23403i	−0.0979117	+	0.301341i
$940$		0			0
$941$	15.6751	+	11.3886i	0.510993	+	0.371258i	0.813200	−	0.581984i	$-0.197723\pi$
$941$	15.6751	+	11.3886i	0.510993	+	0.371258i	−0.302207	+	0.953242i	$0.597723\pi$
$942$	−7.71042	+	23.7302i	−0.251219	+	0.773173i
$943$	2.84609	+	8.75935i	0.0926813	+	0.285244i
$944$	−7.34857	+	5.33905i	−0.239176	+	0.173771i
$945$		0			0
$946$	−1.20122	−	1.28621i	−0.0390551	−	0.0418184i
$947$	27.4774			0.892895			0.446448	−	0.894810i	$-0.352689\pi$
$947$	27.4774			0.892895			0.446448	+	0.894810i	$0.352689\pi$
$948$	−25.5169	+	18.5391i	−0.828750	+	0.602122i
$949$	16.3369	+	50.2798i	0.530318	+	1.63215i
$950$		0			0
$951$	13.8145	+	10.0368i	0.447967	+	0.325467i
$952$	−1.94261	−	1.41139i	−0.0629603	−	0.0457433i
$953$	−4.00753	+	12.3339i	−0.129817	+	0.399534i	−0.994748	−	0.102356i	$-0.967362\pi$
$953$	−4.00753	+	12.3339i	−0.129817	+	0.399534i	0.864931	+	0.501890i	$0.167362\pi$
$954$	−1.78533	−	5.49468i	−0.0578022	−	0.177897i
$955$		0			0
$956$	−29.6230			−0.958075
$957$	1.43013	+	11.5756i	0.0462295	+	0.374185i
$958$	−29.6908			−0.959268
$959$	−7.36890	+	5.35382i	−0.237954	+	0.172884i
$960$		0			0
$961$	21.9294	−	67.4919i	0.707402	−	2.17716i
$962$	77.9889	+	56.6623i	2.51446	+	1.82686i
$963$	4.00964	+	2.91317i	0.129209	+	0.0938757i
$964$	−12.3592	+	38.0376i	−0.398062	+	1.22511i
$965$		0			0
$966$	−12.4815	+	9.06833i	−0.401585	+	0.291769i
$967$	−48.0563			−1.54539			−0.772694	−	0.634779i	$-0.781091\pi$
$967$	−48.0563			−1.54539			−0.772694	+	0.634779i	$0.781091\pi$
$968$	−21.9250	−	34.9702i	−0.704695	−	1.12399i
$969$	2.15320			0.0691708
$970$		0			0
$971$	15.9783	+	49.1760i	0.512766	+	1.57813i	0.787309	+	0.616558i	$0.211473\pi$
$971$	15.9783	+	49.1760i	0.512766	+	1.57813i	−0.274543	+	0.961575i	$0.588527\pi$
$972$	1.10857	−	3.41183i	0.0355574	−	0.109434i
$973$	18.3279	+	13.3160i	0.587566	+	0.426892i
$974$	−3.29370	−	2.39301i	−0.105537	−	0.0766770i
$975$		0			0
$976$	−1.78383	−	5.49005i	−0.0570989	−	0.175732i
$977$	10.3538	−	7.52247i	0.331247	−	0.240665i	−0.409713	−	0.912215i	$-0.634371\pi$
$977$	10.3538	−	7.52247i	0.331247	−	0.240665i	0.740960	+	0.671550i	$0.234371\pi$
$978$	−23.8907			−0.763941
$979$	−6.30571	−	51.0389i	−0.201532	−	1.63121i
$980$		0			0
$981$	2.11693	−	1.53804i	0.0675885	−	0.0491059i
$982$	14.6985	+	45.2373i	0.469048	+	1.44358i
$983$	−4.22705	+	13.0095i	−0.134822	+	0.414940i	−0.995562	−	0.0941048i	$-0.970001\pi$
$983$	−4.22705	+	13.0095i	−0.134822	+	0.414940i	0.860740	+	0.509044i	$0.170001\pi$
$984$	7.34317	+	5.33512i	0.234092	+	0.170078i
$985$		0			0
$986$	0.958929	−	2.95128i	0.0305385	−	0.0939879i
$987$	2.47720	+	7.62403i	0.0788500	+	0.242675i
$988$	−59.1493	+	42.9745i	−1.88179	+	1.36720i
$989$	0.854717			0.0271784
$990$		0			0
$991$	34.7067			1.10250			0.551248	−	0.834342i	$-0.314152\pi$
$991$	34.7067			1.10250			0.551248	+	0.834342i	$0.314152\pi$
$992$	−28.5818	+	20.7659i	−0.907474	+	0.659319i
$993$	−0.864533	−	2.66076i	−0.0274351	−	0.0844366i
$994$	10.9884	−	33.8189i	0.348532	−	1.07267i
$995$		0			0
$996$	−21.5992	−	15.6927i	−0.684395	−	0.497242i
$997$	−9.55310	+	29.4014i	−0.302550	+	0.931153i	0.678030	+	0.735034i	$0.262834\pi$
$997$	−9.55310	+	29.4014i	−0.302550	+	0.931153i	−0.980580	+	0.196119i	$0.937166\pi$
$998$	13.0650	+	40.2099i	0.413565	+	1.27282i
$999$	−9.33763	+	6.78419i	−0.295430	+	0.214642i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.n.p.751.1		24
5.2	odd	4		165.2.s.a.124.2	yes	48
5.3	odd	4		165.2.s.a.124.11	yes	48
5.4	even	2		825.2.n.o.751.6		24
11.2	odd	10		9075.2.a.ea.1.1		12
11.4	even	5	inner	825.2.n.p.301.1		24
11.9	even	5		9075.2.a.dy.1.12		12
15.2	even	4		495.2.ba.c.289.11		48
15.8	even	4		495.2.ba.c.289.2		48
55.2	even	20		1815.2.c.k.364.3		24
55.4	even	10		825.2.n.o.301.6		24
55.9	even	10		9075.2.a.dz.1.1		12
55.13	even	20		1815.2.c.k.364.22		24
55.24	odd	10		9075.2.a.dx.1.12		12
55.37	odd	20		165.2.s.a.4.11	yes	48
55.42	odd	20		1815.2.c.j.364.22		24
55.48	odd	20		165.2.s.a.4.2	✓	48
55.53	odd	20		1815.2.c.j.364.3		24
165.92	even	20		495.2.ba.c.334.2		48
165.158	even	20		495.2.ba.c.334.11		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.s.a.4.2	✓	48	55.48	odd	20
165.2.s.a.4.11	yes	48	55.37	odd	20
165.2.s.a.124.2	yes	48	5.2	odd	4
165.2.s.a.124.11	yes	48	5.3	odd	4
495.2.ba.c.289.2		48	15.8	even	4
495.2.ba.c.289.11		48	15.2	even	4
495.2.ba.c.334.2		48	165.92	even	20
495.2.ba.c.334.11		48	165.158	even	20
825.2.n.o.301.6		24	55.4	even	10
825.2.n.o.751.6		24	5.4	even	2
825.2.n.p.301.1		24	11.4	even	5	inner
825.2.n.p.751.1		24	1.1	even	1	trivial
1815.2.c.j.364.3		24	55.53	odd	20
1815.2.c.j.364.22		24	55.42	odd	20
1815.2.c.k.364.3		24	55.2	even	20
1815.2.c.k.364.22		24	55.13	even	20
9075.2.a.dx.1.12		12	55.24	odd	10
9075.2.a.dy.1.12		12	11.9	even	5
9075.2.a.dz.1.1		12	55.9	even	10
9075.2.a.ea.1.1		12	11.2	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	825.2.n.p.751.1

Level	$825$
Weight	$2$
Character	825.751
Analytic conductor	$6.588$
Analytic rank	$0$
Dimension	$24$
Inner twists	$2$