LMFDB - Embedded newform 588.2.b.d.391.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,2,Mod(391,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.391"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,4,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.15911316233388032.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 10 x^{10} - 20 x^{9} + 35 x^{8} - 56 x^{7} + 84 x^{6} - 112 x^{5} + 140 x^{4} + \cdots + 64 $ x^12 - 4x^11 + 10x^10 - 20x^9 + 35x^8 - 56x^7 + 84x^6 - 112x^5 + 140x^4 - 160x^3 + 160x^2 - 128*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			391.1
Root			$-0.988865 - 1.01101i$ of defining polynomial
Character	$\chi$	$=$	588.391
Dual form			588.2.b.d.391.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.988865 - 1.01101i) q^{2} +1.00000 q^{3} +(-0.0442929 + 1.99951i) q^{4} +1.12886i q^{5} +(-0.988865 - 1.01101i) q^{6} +(2.06533 - 1.93246i) q^{8} +1.00000 q^{9} +(1.14129 - 1.11629i) q^{10} +1.35000i q^{11} +(-0.0442929 + 1.99951i) q^{12} -5.58489i q^{13} +1.12886i q^{15} +(-3.99608 - 0.177128i) q^{16} +3.97347i q^{17} +(-0.988865 - 1.01101i) q^{18} +6.14408 q^{19} +(-2.25717 - 0.0500006i) q^{20} +(1.36487 - 1.33497i) q^{22} +6.61394i q^{23} +(2.06533 - 1.93246i) q^{24} +3.72567 q^{25} +(-5.64640 + 5.52270i) q^{26} +1.00000 q^{27} +8.55270 q^{29} +(1.14129 - 1.11629i) q^{30} -2.92221 q^{31} +(3.77250 + 4.21524i) q^{32} +1.35000i q^{33} +(4.01723 - 3.92923i) q^{34} +(-0.0442929 + 1.99951i) q^{36} +6.32497 q^{37} +(-6.07567 - 6.21175i) q^{38} -5.58489i q^{39} +(2.18149 + 2.33147i) q^{40} -0.149223i q^{41} +10.6557i q^{43} +(-2.69934 - 0.0597956i) q^{44} +1.12886i q^{45} +(6.68678 - 6.54030i) q^{46} -3.59492 q^{47} +(-3.99608 - 0.177128i) q^{48} +(-3.68418 - 3.76670i) q^{50} +3.97347i q^{51} +(11.1670 + 0.247371i) q^{52} +0.733587 q^{53} +(-0.988865 - 1.01101i) q^{54} -1.52397 q^{55} +6.14408 q^{57} +(-8.45746 - 8.64689i) q^{58} -14.4054 q^{59} +(-2.25717 - 0.0500006i) q^{60} -9.11488i q^{61} +(2.88967 + 2.95439i) q^{62} +(0.531167 - 7.98235i) q^{64} +6.30457 q^{65} +(1.36487 - 1.33497i) q^{66} -0.234093i q^{67} +(-7.94500 - 0.175997i) q^{68} +6.61394i q^{69} -8.74104i q^{71} +(2.06533 - 1.93246i) q^{72} -1.76546i q^{73} +(-6.25454 - 6.39463i) q^{74} +3.72567 q^{75} +(-0.272139 + 12.2852i) q^{76} +(-5.64640 + 5.52270i) q^{78} -8.40771i q^{79} +(0.199953 - 4.51102i) q^{80} +1.00000 q^{81} +(-0.150867 + 0.147562i) q^{82} +9.12928 q^{83} -4.48551 q^{85} +(10.7731 - 10.5371i) q^{86} +8.55270 q^{87} +(2.60883 + 2.78820i) q^{88} -7.92746i q^{89} +(1.14129 - 1.11629i) q^{90} +(-13.2246 - 0.292951i) q^{92} -2.92221 q^{93} +(3.55489 + 3.63451i) q^{94} +6.93583i q^{95} +(3.77250 + 4.21524i) q^{96} -6.23063i q^{97} +1.35000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 12 q^{3} - 4 q^{4} + 4 q^{6} + 4 q^{8} + 12 q^{9} - 4 q^{12} - 4 q^{16} + 4 q^{18} - 24 q^{20} + 4 q^{24} - 12 q^{25} + 24 q^{26} + 12 q^{27} + 32 q^{29} + 16 q^{31} + 4 q^{32} + 32 q^{34}+ \cdots + 4 q^{96}+O(q^{100}) $ 12 * q + 4 * q^2 + 12 * q^3 - 4 * q^4 + 4 * q^6 + 4 * q^8 + 12 * q^9 - 4 * q^12 - 4 * q^16 + 4 * q^18 - 24 * q^20 + 4 * q^24 - 12 * q^25 + 24 * q^26 + 12 * q^27 + 32 * q^29 + 16 * q^31 + 4 * q^32 + 32 * q^34 - 4 * q^36 + 32 * q^37 - 24 * q^38 - 32 * q^40 - 24 * q^44 + 24 * q^46 - 4 * q^48 - 28 * q^50 + 32 * q^52 - 32 * q^53 + 4 * q^54 + 16 * q^55 + 16 * q^58 - 16 * q^59 - 24 * q^60 + 8 * q^62 - 4 * q^64 - 8 * q^68 + 4 * q^72 - 32 * q^74 - 12 * q^75 - 32 * q^76 + 24 * q^78 - 16 * q^80 + 12 * q^81 + 32 * q^82 - 16 * q^83 + 16 * q^85 - 24 * q^86 + 32 * q^87 + 24 * q^88 + 16 * q^93 + 4 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−0.988865	−	1.01101i	−0.699233	−	0.714894i
$2$	−0.988865	−	1.01101i	−0.699233	−	0.714894i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−0.0442929	+	1.99951i	−0.0221465	+	0.999755i
$5$			1.12886i			0.504843i	0.967617	+	0.252421i	$0.0812269\pi$
$5$			1.12886i			0.504843i	−0.967617	+	0.252421i	$0.918773\pi$
$6$	−0.988865	−	1.01101i	−0.403702	−	0.412744i
$7$		0			0
$7$		0			0
$8$	2.06533	−	1.93246i	0.730204	−	0.683229i
$9$	1.00000			0.333333
$10$	1.14129	−	1.11629i	0.360909	−	0.353003i
$11$			1.35000i			0.407041i	0.979071	+	0.203521i	$0.0652384\pi$
$11$			1.35000i			0.407041i	−0.979071	+	0.203521i	$0.934762\pi$
$12$	−0.0442929	+	1.99951i	−0.0127863	+	0.577209i
$13$		−	5.58489i		−	1.54897i	−0.632592	−	0.774485i	$-0.718009\pi$
$13$		−	5.58489i		−	1.54897i	0.632592	−	0.774485i	$-0.281991\pi$
$14$		0			0
$15$			1.12886i			0.291471i
$16$	−3.99608	−	0.177128i	−0.999019	−	0.0442821i
$17$			3.97347i			0.963709i	0.876251	+	0.481855i	$0.160037\pi$
$17$			3.97347i			0.963709i	−0.876251	+	0.481855i	$0.839963\pi$
$18$	−0.988865	−	1.01101i	−0.233078	−	0.238298i
$19$	6.14408			1.40955			0.704775	−	0.709431i	$-0.251048\pi$
$19$	6.14408			1.40955			0.704775	+	0.709431i	$0.251048\pi$
$20$	−2.25717	−	0.0500006i	−0.504719	−	0.0111805i
$21$		0			0
$22$	1.36487	−	1.33497i	0.290991	−	0.284617i
$23$			6.61394i			1.37910i	0.724237	+	0.689551i	$0.242192\pi$
$23$			6.61394i			1.37910i	−0.724237	+	0.689551i	$0.757808\pi$
$24$	2.06533	−	1.93246i	0.421584	−	0.394463i
$25$	3.72567			0.745134
$26$	−5.64640	+	5.52270i	−1.10735	+	1.08309i
$27$	1.00000			0.192450
$28$		0			0
$29$	8.55270			1.58820			0.794098	−	0.607790i	$-0.207944\pi$
$29$	8.55270			1.58820			0.794098	+	0.607790i	$0.207944\pi$
$30$	1.14129	−	1.11629i	0.208371	−	0.203806i
$31$	−2.92221			−0.524845			−0.262422	−	0.964953i	$-0.584521\pi$
$31$	−2.92221			−0.524845			−0.262422	+	0.964953i	$0.584521\pi$
$32$	3.77250	+	4.21524i	0.666890	+	0.745156i
$33$			1.35000i			0.235005i
$34$	4.01723	−	3.92923i	0.688950	−	0.673857i
$35$		0			0
$36$	−0.0442929	+	1.99951i	−0.00738215	+	0.333252i
$37$	6.32497			1.03982			0.519910	−	0.854221i	$-0.325966\pi$
$37$	6.32497			1.03982			0.519910	+	0.854221i	$0.325966\pi$
$38$	−6.07567	−	6.21175i	−0.985603	−	1.00768i
$39$		−	5.58489i		−	0.894298i
$40$	2.18149	+	2.33147i	0.344923	+	0.368638i
$41$		−	0.149223i		−	0.0233048i	−0.999932	−	0.0116524i	$-0.996291\pi$
$41$		−	0.149223i		−	0.0233048i	0.999932	−	0.0116524i	$-0.00370916\pi$
$42$		0			0
$43$			10.6557i			1.62498i	0.582974	+	0.812491i	$0.301889\pi$
$43$			10.6557i			1.62498i	−0.582974	+	0.812491i	$0.698111\pi$
$44$	−2.69934	−	0.0597956i	−0.406942	−	0.00901452i
$45$			1.12886i			0.168281i
$46$	6.68678	−	6.54030i	0.985912	−	0.964314i
$47$	−3.59492			−0.524373			−0.262186	−	0.965017i	$-0.584444\pi$
$47$	−3.59492			−0.524373			−0.262186	+	0.965017i	$0.584444\pi$
$48$	−3.99608	−	0.177128i	−0.576784	−	0.0255663i
$49$		0			0
$50$	−3.68418	−	3.76670i	−0.521022	−	0.532692i
$51$			3.97347i			0.556398i
$52$	11.1670	+	0.247371i	1.54859	+	0.0343042i
$53$	0.733587			0.100766			0.0503830	−	0.998730i	$-0.483956\pi$
$53$	0.733587			0.100766			0.0503830	+	0.998730i	$0.483956\pi$
$54$	−0.988865	−	1.01101i	−0.134567	−	0.137581i
$55$	−1.52397			−0.205492
$56$		0			0
$57$	6.14408			0.813804
$58$	−8.45746	−	8.64689i	−1.11052	−	1.13539i
$59$	−14.4054			−1.87542			−0.937712	−	0.347415i	$-0.887060\pi$
$59$	−14.4054			−1.87542			−0.937712	+	0.347415i	$0.887060\pi$
$60$	−2.25717	−	0.0500006i	−0.291400	−	0.00645505i
$61$		−	9.11488i		−	1.16704i	−0.812098	−	0.583520i	$-0.801675\pi$
$61$		−	9.11488i		−	1.16704i	0.812098	−	0.583520i	$-0.198325\pi$
$62$	2.88967	+	2.95439i	0.366989	+	0.375208i
$63$		0			0
$64$	0.531167	−	7.98235i	0.0663959	−	0.997793i
$65$	6.30457			0.781986
$66$	1.36487	−	1.33497i	0.168004	−	0.164324i
$67$		−	0.234093i		−	0.0285990i	−0.999898	−	0.0142995i	$-0.995448\pi$
$67$		−	0.234093i		−	0.0285990i	0.999898	−	0.0142995i	$-0.00455182\pi$
$68$	−7.94500	−	0.175997i	−0.963473	−	0.0213427i
$69$			6.61394i			0.796225i
$70$		0			0
$71$		−	8.74104i		−	1.03737i	−0.854965	−	0.518685i	$-0.826422\pi$
$71$		−	8.74104i		−	1.03737i	0.854965	−	0.518685i	$-0.173578\pi$
$72$	2.06533	−	1.93246i	0.243401	−	0.227743i
$73$		−	1.76546i		−	0.206631i	−0.994649	−	0.103316i	$-0.967055\pi$
$73$		−	1.76546i		−	0.206631i	0.994649	−	0.103316i	$-0.0329452\pi$
$74$	−6.25454	−	6.39463i	−0.727076	−	0.743360i
$75$	3.72567			0.430203
$76$	−0.272139	+	12.2852i	−0.0312165	+	1.40920i
$77$		0			0
$78$	−5.64640	+	5.52270i	−0.639328	+	0.625323i
$79$		−	8.40771i		−	0.945941i	−0.881078	−	0.472971i	$-0.843182\pi$
$79$		−	8.40771i		−	0.945941i	0.881078	−	0.472971i	$-0.156818\pi$
$80$	0.199953	−	4.51102i	0.0223555	−	0.504348i
$81$	1.00000			0.111111
$82$	−0.150867	+	0.147562i	−0.0166604	+	0.0162955i
$83$	9.12928			1.00207			0.501035	−	0.865427i	$-0.332953\pi$
$83$	9.12928			1.00207			0.501035	+	0.865427i	$0.332953\pi$
$84$		0			0
$85$	−4.48551			−0.486522
$86$	10.7731	−	10.5371i	1.16169	−	1.13624i
$87$	8.55270			0.916945
$88$	2.60883	+	2.78820i	0.278102	+	0.297223i
$89$		−	7.92746i		−	0.840309i	−0.907453	−	0.420155i	$-0.861976\pi$
$89$		−	7.92746i		−	0.840309i	0.907453	−	0.420155i	$-0.138024\pi$
$90$	1.14129	−	1.11629i	0.120303	−	0.117668i
$91$		0			0
$92$	−13.2246	−	0.292951i	−1.37876	−	0.0305422i
$93$	−2.92221			−0.303019
$94$	3.55489	+	3.63451i	0.366659	+	0.374871i
$95$			6.93583i			0.711601i
$96$	3.77250	+	4.21524i	0.385029	+	0.430216i
$97$		−	6.23063i		−	0.632624i	−0.948655	−	0.316312i	$-0.897555\pi$
$97$		−	6.23063i		−	0.632624i	0.948655	−	0.316312i	$-0.102445\pi$
$98$		0			0
$99$			1.35000i			0.135680i
$100$	−0.165021	+	7.44951i	−0.0165021	+	0.744951i
$101$			0.794961i			0.0791016i	0.999218	+	0.0395508i	$0.0125927\pi$
$101$			0.794961i			0.0791016i	−0.999218	+	0.0395508i	$0.987407\pi$
$102$	4.01723	−	3.92923i	0.397765	−	0.389052i
$103$	3.35476			0.330554			0.165277	−	0.986247i	$-0.447148\pi$
$103$	3.35476			0.330554			0.165277	+	0.986247i	$0.447148\pi$
$104$	−10.7926	−	11.5346i	−1.05830	−	1.13106i
$105$		0			0
$106$	−0.725418	−	0.741666i	−0.0704589	−	0.0720369i
$107$			12.5510i			1.21335i	0.794950	+	0.606675i	$0.207497\pi$
$107$			12.5510i			1.21335i	−0.794950	+	0.606675i	$0.792503\pi$
$108$	−0.0442929	+	1.99951i	−0.00426209	+	0.192403i
$109$	−15.2532			−1.46099			−0.730496	−	0.682917i	$-0.760711\pi$
$109$	−15.2532			−1.46099			−0.730496	+	0.682917i	$0.760711\pi$
$110$	1.50700	+	1.54075i	0.143687	+	0.146905i
$111$	6.32497			0.600340
$112$		0			0
$113$	−11.7783			−1.10801			−0.554004	−	0.832514i	$-0.686901\pi$
$113$	−11.7783			−1.10801			−0.554004	+	0.832514i	$0.686901\pi$
$114$	−6.07567	−	6.21175i	−0.569038	−	0.581783i
$115$	−7.46623			−0.696230
$116$	−0.378824	+	17.1012i	−0.0351729	+	1.58781i
$117$		−	5.58489i		−	0.516323i
$118$	14.2450	+	14.5640i	1.31136	+	1.34073i
$119$		0			0
$120$	2.18149	+	2.33147i	0.199142	+	0.212833i
$121$	9.17749			0.834317
$122$	−9.21526	+	9.01338i	−0.834310	+	0.816033i
$123$		−	0.149223i		−	0.0134550i
$124$	0.129433	−	5.84299i	0.0116234	−	0.524716i
$125$			9.85008i			0.881018i
$126$		0			0
$127$			3.52444i			0.312743i	0.987698	+	0.156372i	$0.0499798\pi$
$127$			3.52444i			0.312743i	−0.987698	+	0.156372i	$0.950020\pi$
$128$	−8.59551	+	7.35644i	−0.759743	+	0.650224i
$129$			10.6557i			0.938184i
$130$	−6.23437	−	6.37400i	−0.546791	−	0.559037i
$131$	−2.37199			−0.207242			−0.103621	−	0.994617i	$-0.533043\pi$
$131$	−2.37199			−0.207242			−0.103621	+	0.994617i	$0.533043\pi$
$132$	−2.69934	−	0.0597956i	−0.234948	−	0.00520454i
$133$		0			0
$134$	−0.236671	+	0.231486i	−0.0204452	+	0.0199973i
$135$			1.12886i			0.0971570i
$136$	7.67860	+	8.20653i	0.658434	+	0.703704i
$137$	−7.17561			−0.613054			−0.306527	−	0.951862i	$-0.599167\pi$
$137$	−7.17561			−0.613054			−0.306527	+	0.951862i	$0.599167\pi$
$138$	6.68678	−	6.54030i	0.569217	−	0.556747i
$139$	−22.5888			−1.91595			−0.957977	−	0.286845i	$-0.907394\pi$
$139$	−22.5888			−1.91595			−0.957977	+	0.286845i	$0.907394\pi$
$140$		0			0
$141$	−3.59492			−0.302747
$142$	−8.83730	+	8.64371i	−0.741610	+	0.725364i
$143$	7.53962			0.630495
$144$	−3.99608	−	0.177128i	−0.333006	−	0.0147607i
$145$			9.65482i			0.801789i
$146$	−1.78490	+	1.74580i	−0.147719	+	0.144483i
$147$		0			0
$148$	−0.280151	+	12.6468i	−0.0230283	+	1.03956i
$149$	−11.0506			−0.905304			−0.452652	−	0.891687i	$-0.649522\pi$
$149$	−11.0506			−0.905304			−0.452652	+	0.891687i	$0.649522\pi$
$150$	−3.68418	−	3.76670i	−0.300812	−	0.307550i
$151$			1.53950i			0.125283i	0.998036	+	0.0626413i	$0.0199524\pi$
$151$			1.53950i			0.125283i	−0.998036	+	0.0626413i	$0.980048\pi$
$152$	12.6896	−	11.8732i	1.02926	−	0.963045i
$153$			3.97347i			0.321236i
$154$		0			0
$155$		−	3.29878i		−	0.264964i
$156$	11.1670	+	0.247371i	0.894079	+	0.0198055i
$157$		−	8.55948i		−	0.683121i	−0.939860	−	0.341560i	$-0.889045\pi$
$157$		−	8.55948i		−	0.683121i	0.939860	−	0.341560i	$-0.110955\pi$
$158$	−8.50030	+	8.31409i	−0.676248	+	0.661433i
$159$	0.733587			0.0581772
$160$	−4.75843	+	4.25863i	−0.376187	+	0.336675i
$161$		0			0
$162$	−0.988865	−	1.01101i	−0.0776926	−	0.0794327i
$163$			5.65996i			0.443323i	0.975124	+	0.221661i	$0.0711479\pi$
$163$			5.65996i			0.443323i	−0.975124	+	0.221661i	$0.928852\pi$
$164$	0.298374	+	0.00660954i	0.0232991	+	0.000516118i
$165$	−1.52397			−0.118641
$166$	−9.02763	−	9.22982i	−0.700680	−	0.716373i
$167$	4.84357			0.374807			0.187403	−	0.982283i	$-0.439993\pi$
$167$	4.84357			0.374807			0.187403	+	0.982283i	$0.439993\pi$
$168$		0			0
$169$	−18.1910			−1.39931
$170$	4.43556	+	4.53490i	0.340192	+	0.347811i
$171$	6.14408			0.469850
$172$	−21.3062	−	0.471973i	−1.62458	−	0.0359876i
$173$		−	2.10368i		−	0.159940i	−0.996797	−	0.0799701i	$-0.974518\pi$
$173$		−	2.10368i		−	0.159940i	0.996797	−	0.0799701i	$-0.0254825\pi$
$174$	−8.45746	−	8.64689i	−0.641159	−	0.655519i
$175$		0			0
$176$	0.239124	−	5.39472i	0.0180246	−	0.406642i
$177$	−14.4054			−1.08278
$178$	−8.01476	+	7.83919i	−0.600732	+	0.587572i
$179$		−	4.00769i		−	0.299549i	−0.988720	−	0.149774i	$-0.952145\pi$
$179$		−	4.00769i		−	0.299549i	0.988720	−	0.149774i	$-0.0478547\pi$
$180$	−2.25717	−	0.0500006i	−0.168240	−	0.00372683i
$181$		−	5.89663i		−	0.438293i	−0.975692	−	0.219146i	$-0.929673\pi$
$181$		−	5.89663i		−	0.438293i	0.975692	−	0.219146i	$-0.0703272\pi$
$182$		0			0
$183$		−	9.11488i		−	0.673791i
$184$	12.7812	+	13.6600i	0.942243	+	1.00703i
$185$			7.14002i			0.524945i
$186$	2.88967	+	2.95439i	0.211881	+	0.216627i
$187$	−5.36420			−0.392269
$188$	0.159229	−	7.18808i	0.0116130	−	0.524244i
$189$		0			0
$190$	7.01221	−	6.85859i	0.508719	−	0.497575i
$191$		−	25.3919i		−	1.83729i	−0.395084	−	0.918645i	$-0.629284\pi$
$191$		−	25.3919i		−	1.83729i	0.395084	−	0.918645i	$-0.370716\pi$
$192$	0.531167	−	7.98235i	0.0383337	−	0.576076i
$193$	0.0733869			0.00528250			0.00264125	−	0.999997i	$-0.499159\pi$
$193$	0.0733869			0.00528250			0.00264125	+	0.999997i	$0.499159\pi$
$194$	−6.29924	+	6.16125i	−0.452259	+	0.442352i
$195$	6.30457			0.451480
$196$		0			0
$197$	7.23506			0.515477			0.257739	−	0.966215i	$-0.417023\pi$
$197$	7.23506			0.515477			0.257739	+	0.966215i	$0.417023\pi$
$198$	1.36487	−	1.33497i	0.0969971	−	0.0948722i
$199$	15.3120			1.08544			0.542718	−	0.839915i	$-0.317395\pi$
$199$	15.3120			1.08544			0.542718	+	0.839915i	$0.317395\pi$
$200$	7.69473	−	7.19972i	0.544100	−	0.509097i
$201$		−	0.234093i		−	0.0165116i
$202$	0.803715	−	0.786109i	0.0565492	−	0.0553104i
$203$		0			0
$204$	−7.94500	−	0.175997i	−0.556261	−	0.0123222i
$205$	0.168453			0.0117653
$206$	−3.31740	−	3.39170i	−0.231134	−	0.236311i
$207$			6.61394i			0.459701i
$208$	−0.989242	+	22.3177i	−0.0685916	+	1.54745i
$209$			8.29453i			0.573745i
$210$		0			0
$211$			13.7540i			0.946861i	0.880831	+	0.473431i	$0.156985\pi$
$211$			13.7540i			0.946861i	−0.880831	+	0.473431i	$0.843015\pi$
$212$	−0.0324927	+	1.46681i	−0.00223161	+	0.100741i
$213$		−	8.74104i		−	0.598926i
$214$	12.6892	−	12.4112i	0.867417	−	0.848415i
$215$	−12.0288			−0.820360
$216$	2.06533	−	1.93246i	0.140528	−	0.131488i
$217$		0			0
$218$	15.0833	+	15.4212i	1.02157	+	1.04445i
$219$		−	1.76546i		−	0.119299i
$220$	0.0675010	−	3.04719i	0.00455092	−	0.205441i
$221$	22.1914			1.49276
$222$	−6.25454	−	6.39463i	−0.419777	−	0.429179i
$223$	−16.4120			−1.09903			−0.549516	−	0.835483i	$-0.685188\pi$
$223$	−16.4120			−1.09903			−0.549516	+	0.835483i	$0.685188\pi$
$224$		0			0
$225$	3.72567			0.248378
$226$	11.6471	+	11.9080i	0.774756	+	0.792108i
$227$	16.1319			1.07071			0.535356	−	0.844627i	$-0.320178\pi$
$227$	16.1319			1.07071			0.535356	+	0.844627i	$0.320178\pi$
$228$	−0.272139	+	12.2852i	−0.0180229	+	0.813604i
$229$			21.6682i			1.43187i	0.698165	+	0.715937i	$0.254000\pi$
$229$			21.6682i			1.43187i	−0.698165	+	0.715937i	$0.746000\pi$
$230$	7.38310	+	7.54846i	0.486827	+	0.497731i
$231$		0			0
$232$	17.6641	−	16.5278i	1.15971	−	1.08510i
$233$	−19.0312			−1.24678			−0.623389	−	0.781912i	$-0.714245\pi$
$233$	−19.0312			−1.24678			−0.623389	+	0.781912i	$0.714245\pi$
$234$	−5.64640	+	5.52270i	−0.369116	+	0.361030i
$235$		−	4.05817i		−	0.264726i
$236$	0.638057	−	28.8037i	0.0415340	−	1.87496i
$237$		−	8.40771i		−	0.546139i
$238$		0			0
$239$		−	15.6878i		−	1.01476i	−0.861722	−	0.507381i	$-0.830614\pi$
$239$		−	15.6878i		−	1.01476i	0.861722	−	0.507381i	$-0.169386\pi$
$240$	0.199953	−	4.51102i	0.0129069	−	0.291185i
$241$		−	11.9011i		−	0.766615i	−0.923621	−	0.383307i	$-0.874785\pi$
$241$		−	11.9011i		−	0.766615i	0.923621	−	0.383307i	$-0.125215\pi$
$242$	−9.07530	−	9.27856i	−0.583382	−	0.596448i
$243$	1.00000			0.0641500
$244$	18.2253	+	0.403725i	1.16675	+	0.0258458i
$245$		0			0
$246$	−0.150867	+	0.147562i	−0.00961891	+	0.00940820i
$247$		−	34.3140i		−	2.18335i
$248$	−6.03533	+	5.64707i	−0.383244	+	0.358589i
$249$	9.12928			0.578545
$250$	9.95856	−	9.74040i	0.629834	−	0.616037i
$251$	−1.68715			−0.106492			−0.0532459	−	0.998581i	$-0.516957\pi$
$251$	−1.68715			−0.106492			−0.0532459	+	0.998581i	$0.516957\pi$
$252$		0			0
$253$	−8.92885			−0.561352
$254$	3.56325	−	3.48519i	0.223578	−	0.218681i
$255$	−4.48551			−0.280893
$256$	15.9373	+	1.41564i	0.996078	+	0.0884772i
$257$			21.3171i			1.32972i	0.746966	+	0.664862i	$0.231510\pi$
$257$			21.3171i			1.32972i	−0.746966	+	0.664862i	$0.768490\pi$
$258$	10.7731	−	10.5371i	0.670702	−	0.656009i
$259$		0			0
$260$	−0.279248	+	12.6061i	−0.0173182	+	0.781794i
$261$	8.55270			0.529399
$262$	2.34558	+	2.39811i	0.144910	+	0.148156i
$263$		−	11.5846i		−	0.714337i	−0.934040	−	0.357169i	$-0.883742\pi$
$263$		−	11.5846i		−	0.714337i	0.934040	−	0.357169i	$-0.116258\pi$
$264$	2.60883	+	2.78820i	0.160563	+	0.171602i
$265$			0.828119i			0.0508709i
$266$		0			0
$267$		−	7.92746i		−	0.485153i
$268$	0.468070	+	0.0103686i	0.0285919	+	0.000633366i
$269$		−	7.25350i		−	0.442254i	−0.975245	−	0.221127i	$-0.929027\pi$
$269$		−	7.25350i		−	0.442254i	0.975245	−	0.221127i	$-0.0709735\pi$
$270$	1.14129	−	1.11629i	0.0694570	−	0.0679354i
$271$	−29.0144			−1.76250			−0.881249	−	0.472653i	$-0.843296\pi$
$271$	−29.0144			−1.76250			−0.881249	+	0.472653i	$0.843296\pi$
$272$	0.703814	−	15.8783i	0.0426750	−	0.962764i
$273$		0			0
$274$	7.09571	+	7.25463i	0.428667	+	0.438268i
$275$			5.02967i			0.303300i
$276$	−13.2246	−	0.292951i	−0.796030	−	0.0176336i
$277$	−0.345141			−0.0207375			−0.0103688	−	0.999946i	$-0.503301\pi$
$277$	−0.345141			−0.0207375			−0.0103688	+	0.999946i	$0.503301\pi$
$278$	22.3372	+	22.8375i	1.33970	+	1.36970i
$279$	−2.92221			−0.174948
$280$		0			0
$281$	6.62734			0.395354			0.197677	−	0.980267i	$-0.436660\pi$
$281$	6.62734			0.395354			0.197677	+	0.980267i	$0.436660\pi$
$282$	3.55489	+	3.63451i	0.211691	+	0.216432i
$283$	−27.7813			−1.65143			−0.825713	−	0.564090i	$-0.809227\pi$
$283$	−27.7813			−1.65143			−0.825713	+	0.564090i	$0.809227\pi$
$284$	17.4778	+	0.387166i	1.03712	+	0.0229741i
$285$			6.93583i			0.410843i
$286$	−7.45567	−	7.62265i	−0.440863	−	0.450737i
$287$		0			0
$288$	3.77250	+	4.21524i	0.222297	+	0.248385i
$289$	1.21150			0.0712647
$290$	9.76115	−	9.54731i	0.573194	−	0.560638i
$291$		−	6.23063i		−	0.365246i
$292$	3.53005	+	0.0781973i	0.206581	+	0.00457615i
$293$			7.28491i			0.425589i	0.977097	+	0.212794i	$0.0682565\pi$
$293$			7.28491i			0.425589i	−0.977097	+	0.212794i	$0.931744\pi$
$294$		0			0
$295$		−	16.2617i		−	0.946794i
$296$	13.0631	−	12.2228i	0.759280	−	0.710435i
$297$			1.35000i			0.0783351i
$298$	10.9276	+	11.1723i	0.633018	+	0.647196i
$299$	36.9382			2.13619
$300$	−0.165021	+	7.44951i	−0.00952748	+	0.430098i
$301$		0			0
$302$	1.55645	−	1.52236i	0.0895638	−	0.0876018i
$303$			0.794961i			0.0456693i
$304$	−24.5522	−	1.08829i	−1.40817	−	0.0624177i
$305$	10.2894			0.589172
$306$	4.01723	−	3.92923i	0.229650	−	0.224619i
$307$	27.1911			1.55188			0.775939	−	0.630808i	$-0.217276\pi$
$307$	27.1911			1.55188			0.775939	+	0.630808i	$0.217276\pi$
$308$		0			0
$309$	3.35476			0.190846
$310$	−3.33510	+	3.26204i	−0.189421	+	0.185272i
$311$	20.9218			1.18636			0.593182	−	0.805068i	$-0.297871\pi$
$311$	20.9218			1.18636			0.593182	+	0.805068i	$0.297871\pi$
$312$	−10.7926	−	11.5346i	−0.611011	−	0.653020i
$313$		−	2.61741i		−	0.147945i	−0.997260	−	0.0739724i	$-0.976432\pi$
$313$		−	2.61741i		−	0.147945i	0.997260	−	0.0739724i	$-0.0235677\pi$
$314$	−8.65374	+	8.46417i	−0.488359	+	0.477661i
$315$		0			0
$316$	16.8113	+	0.372402i	0.945709	+	0.0209492i
$317$	−12.9486			−0.727266			−0.363633	−	0.931542i	$-0.618464\pi$
$317$	−12.9486			−0.727266			−0.363633	+	0.931542i	$0.618464\pi$
$318$	−0.725418	−	0.741666i	−0.0406794	−	0.0415905i
$319$			11.5462i			0.646461i
$320$	9.01097	+	0.599615i	0.503729	+	0.0335195i
$321$			12.5510i			0.700528i
$322$		0			0
$323$			24.4134i			1.35840i
$324$	−0.0442929	+	1.99951i	−0.00246072	+	0.111084i
$325$		−	20.8075i		−	1.15419i
$326$	5.72229	−	5.59694i	0.316929	−	0.309986i
$327$	−15.2532			−0.843504
$328$	−0.288369	−	0.308195i	−0.0159225	−	0.0170172i
$329$		0			0
$330$	1.50700	+	1.54075i	0.0829575	+	0.0848156i
$331$			5.23999i			0.288016i	0.989577	+	0.144008i	$0.0459991\pi$
$331$			5.23999i			0.288016i	−0.989577	+	0.144008i	$0.954001\pi$
$332$	−0.404363	+	18.2541i	−0.0221923	+	1.00182i
$333$	6.32497			0.346606
$334$	−4.78963	−	4.89691i	−0.262077	−	0.267947i
$335$	0.264258			0.0144380
$336$		0			0
$337$	21.6837			1.18119			0.590594	−	0.806969i	$-0.298894\pi$
$337$	21.6837			1.18119			0.590594	+	0.806969i	$0.298894\pi$
$338$	17.9884	+	18.3913i	0.978443	+	1.00036i
$339$	−11.7783			−0.639709
$340$	0.198676	−	8.96881i	0.0107747	−	0.486402i
$341$		−	3.94500i		−	0.213633i
$342$	−6.07567	−	6.21175i	−0.328534	−	0.335893i
$343$		0			0
$344$	20.5918	+	22.0076i	1.11024	+	1.18657i
$345$	−7.46623			−0.401969
$346$	−2.12685	+	2.08026i	−0.114340	+	0.111835i
$347$		−	0.655611i		−	0.0351951i	−0.999845	−	0.0175975i	$-0.994398\pi$
$347$		−	0.655611i		−	0.0351951i	0.999845	−	0.0175975i	$-0.00560176\pi$
$348$	−0.378824	+	17.1012i	−0.0203071	+	0.916721i
$349$		−	19.4157i		−	1.03930i	−0.854380	−	0.519649i	$-0.826063\pi$
$349$		−	19.4157i		−	1.03930i	0.854380	−	0.519649i	$-0.173937\pi$
$350$		0			0
$351$		−	5.58489i		−	0.298099i
$352$	−5.69059	+	5.09289i	−0.303309	+	0.271452i
$353$		−	29.8844i		−	1.59058i	−0.606226	−	0.795292i	$-0.707317\pi$
$353$		−	29.8844i		−	1.59058i	0.606226	−	0.795292i	$-0.292683\pi$
$354$	14.2450	+	14.5640i	0.757113	+	0.774070i
$355$	9.86743			0.523709
$356$	15.8510	+	0.351130i	0.840103	+	0.0186099i
$357$		0			0
$358$	−4.05182	+	3.96306i	−0.214145	+	0.209454i
$359$		−	12.5933i		−	0.664650i	−0.943165	−	0.332325i	$-0.892167\pi$
$359$		−	12.5933i		−	0.664650i	0.943165	−	0.332325i	$-0.107833\pi$
$360$	2.18149	+	2.33147i	0.114974	+	0.122879i
$361$	18.7498			0.986830
$362$	−5.96156	+	5.83097i	−0.313333	+	0.306469i
$363$	9.17749			0.481693
$364$		0			0
$365$	1.99296			0.104316
$366$	−9.21526	+	9.01338i	−0.481689	+	0.471137i
$367$	5.46893			0.285476			0.142738	−	0.989761i	$-0.454409\pi$
$367$	5.46893			0.285476			0.142738	+	0.989761i	$0.454409\pi$
$368$	1.17152	−	26.4298i	0.0610695	−	1.37775i
$369$		−	0.149223i		−	0.00776826i
$370$	7.21866	−	7.06052i	0.375280	−	0.367059i
$371$		0			0
$372$	0.129433	−	5.84299i	0.00671080	−	0.302945i
$373$	−14.8481			−0.768805			−0.384402	−	0.923166i	$-0.625592\pi$
$373$	−14.8481			−0.768805			−0.384402	+	0.923166i	$0.625592\pi$
$374$	5.30447	+	5.42328i	0.274288	+	0.280431i
$375$			9.85008i			0.508656i
$376$	−7.42469	+	6.94705i	−0.382899	+	0.358267i
$377$		−	47.7659i		−	2.46007i
$378$		0			0
$379$		−	30.6135i		−	1.57251i	−0.617901	−	0.786256i	$-0.712017\pi$
$379$		−	30.6135i		−	1.57251i	0.617901	−	0.786256i	$-0.287983\pi$
$380$	−13.8683	−	0.307208i	−0.711426	−	0.0157594i
$381$			3.52444i			0.180562i
$382$	−25.6715	+	25.1091i	−1.31347	+	1.28469i
$383$	−23.4784			−1.19969			−0.599844	−	0.800117i	$-0.704771\pi$
$383$	−23.4784			−1.19969			−0.599844	+	0.800117i	$0.704771\pi$
$384$	−8.59551	+	7.35644i	−0.438638	+	0.375407i
$385$		0			0
$386$	−0.0725697	−	0.0741951i	−0.00369370	−	0.00377643i
$387$			10.6557i			0.541661i
$388$	12.4582	+	0.275973i	0.632469	+	0.0140104i
$389$	−36.1774			−1.83427			−0.917134	−	0.398579i	$-0.869503\pi$
$389$	−36.1774			−1.83427			−0.917134	+	0.398579i	$0.869503\pi$
$390$	−6.23437	−	6.37400i	−0.315690	−	0.322760i
$391$	−26.2803			−1.32905
$392$		0			0
$393$	−2.37199			−0.119651
$394$	−7.15450	−	7.31474i	−0.360439	−	0.368511i
$395$	9.49115			0.477552
$396$	−2.69934	−	0.0597956i	−0.135647	−	0.00300484i
$397$		−	1.33174i		−	0.0668379i	−0.999441	−	0.0334189i	$-0.989360\pi$
$397$		−	1.33174i		−	0.0668379i	0.999441	−	0.0334189i	$-0.0106396\pi$
$398$	−15.1415	−	15.4806i	−0.758973	−	0.775971i
$399$		0			0
$400$	−14.8881	−	0.659921i	−0.744403	−	0.0329961i
$401$	26.0596			1.30135			0.650677	−	0.759355i	$-0.274485\pi$
$401$	26.0596			1.30135			0.650677	+	0.759355i	$0.274485\pi$
$402$	−0.236671	+	0.231486i	−0.0118041	+	0.0115455i
$403$			16.3202i			0.812969i
$404$	−1.58953	−	0.0352111i	−0.0790822	−	0.00175182i
$405$			1.12886i			0.0560936i
$406$		0			0
$407$			8.53873i			0.423249i
$408$	7.67860	+	8.20653i	0.380147	+	0.406284i
$409$			13.3209i			0.658675i	0.944212	+	0.329337i	$0.106825\pi$
$409$			13.3209i			0.658675i	−0.944212	+	0.329337i	$0.893175\pi$
$410$	−0.166577	−	0.170308i	−0.00822665	−	0.00841091i
$411$	−7.17561			−0.353947
$412$	−0.148592	+	6.70787i	−0.00732060	+	0.330473i
$413$		0			0
$414$	6.68678	−	6.54030i	0.328637	−	0.321438i
$415$			10.3057i			0.505887i
$416$	23.5417	−	21.0690i	1.15422	−	1.03299i
$417$	−22.5888			−1.10618
$418$	8.38588	−	8.20217i	0.410167	−	0.401181i
$419$	−7.54663			−0.368677			−0.184339	−	0.982863i	$-0.559014\pi$
$419$	−7.54663			−0.368677			−0.184339	+	0.982863i	$0.559014\pi$
$420$		0			0
$421$	2.67060			0.130157			0.0650785	−	0.997880i	$-0.479270\pi$
$421$	2.67060			0.130157			0.0650785	+	0.997880i	$0.479270\pi$
$422$	13.9054	−	13.6008i	0.676905	−	0.662076i
$423$	−3.59492			−0.174791
$424$	1.51510	−	1.41763i	0.0735797	−	0.0688462i
$425$			14.8039i			0.718092i
$426$	−8.83730	+	8.64371i	−0.428169	+	0.418789i
$427$		0			0
$428$	−25.0958	−	0.555920i	−1.21305	−	0.0268714i
$429$	7.53962			0.364016
$430$	11.8949	+	12.1613i	0.573623	+	0.586471i
$431$		−	11.8862i		−	0.572539i	−0.958149	−	0.286269i	$-0.907585\pi$
$431$		−	11.8862i		−	0.572539i	0.958149	−	0.286269i	$-0.0924152\pi$
$432$	−3.99608	−	0.177128i	−0.192261	−	0.00852208i
$433$			20.6667i			0.993177i	0.867986	+	0.496589i	$0.165414\pi$
$433$			20.6667i			0.993177i	−0.867986	+	0.496589i	$0.834586\pi$
$434$		0			0
$435$			9.65482i			0.462913i
$436$	0.675609	−	30.4989i	0.0323558	−	1.46063i
$437$			40.6366i			1.94391i
$438$	−1.78490	+	1.74580i	−0.0852858	+	0.0834175i
$439$	5.42064			0.258713			0.129356	−	0.991598i	$-0.458709\pi$
$439$	5.42064			0.258713			0.129356	+	0.991598i	$0.458709\pi$
$440$	−3.14750	+	2.94501i	−0.150051	+	0.140398i
$441$		0			0
$442$	−21.9443	−	22.4358i	−1.04378	−	1.06716i
$443$			22.7038i			1.07869i	0.842085	+	0.539344i	$0.181328\pi$
$443$			22.7038i			1.07869i	−0.842085	+	0.539344i	$0.818672\pi$
$444$	−0.280151	+	12.6468i	−0.0132954	+	0.600193i
$445$	8.94902			0.424224
$446$	16.2293	+	16.5928i	0.768479	+	0.785691i
$447$	−11.0506			−0.522677
$448$		0			0
$449$	−15.6516			−0.738645			−0.369322	−	0.929301i	$-0.620410\pi$
$449$	−15.6516			−0.738645			−0.369322	+	0.929301i	$0.620410\pi$
$450$	−3.68418	−	3.76670i	−0.173674	−	0.177564i
$451$	0.201452			0.00948601
$452$	0.521695	−	23.5508i	0.0245385	−	1.10774i
$453$			1.53950i			0.0723320i
$454$	−15.9523	−	16.3095i	−0.748677	−	0.765445i
$455$		0			0
$456$	12.6896	−	11.8732i	0.594243	−	0.556014i
$457$	−17.0266			−0.796469			−0.398235	−	0.917284i	$-0.630377\pi$
$457$	−17.0266			−0.796469			−0.398235	+	0.917284i	$0.630377\pi$
$458$	21.9068	−	21.4269i	1.02364	−	1.00121i
$459$			3.97347i			0.185466i
$460$	0.330701	−	14.9288i	0.0154190	−	0.696059i
$461$			38.1090i			1.77491i	0.460891	+	0.887457i	$0.347530\pi$
$461$			38.1090i			1.77491i	−0.460891	+	0.887457i	$0.652470\pi$
$462$		0			0
$463$			1.38958i			0.0645794i	0.999479	+	0.0322897i	$0.0102799\pi$
$463$			1.38958i			0.0645794i	−0.999479	+	0.0322897i	$0.989720\pi$
$464$	−34.1772	−	1.51492i	−1.58664	−	0.0703286i
$465$		−	3.29878i		−	0.152977i
$466$	18.8193	+	19.2408i	0.871788	+	0.891313i
$467$	−3.49381			−0.161674			−0.0808372	−	0.996727i	$-0.525759\pi$
$467$	−3.49381			−0.161674			−0.0808372	+	0.996727i	$0.525759\pi$
$468$	11.1670	+	0.247371i	0.516197	+	0.0114347i
$469$		0			0
$470$	−4.10286	+	4.01298i	−0.189251	+	0.185105i
$471$		−	8.55948i		−	0.394400i
$472$	−29.7519	+	27.8379i	−1.36944	+	1.28134i
$473$	−14.3853			−0.661435
$474$	−8.50030	+	8.31409i	−0.390432	+	0.381879i
$475$	22.8908			1.05030
$476$		0			0
$477$	0.733587			0.0335886
$478$	−15.8606	+	15.5132i	−0.725447	+	0.709555i
$479$	13.7216			0.626955			0.313478	−	0.949596i	$-0.398506\pi$
$479$	13.7216			0.626955			0.313478	+	0.949596i	$0.398506\pi$
$480$	−4.75843	+	4.25863i	−0.217191	+	0.194379i
$481$		−	35.3243i		−	1.61065i
$482$	−12.0321	+	11.7685i	−0.548048	+	0.536042i
$483$		0			0
$484$	−0.406498	+	18.3505i	−0.0184772	+	0.834113i
$485$	7.03352			0.319376
$486$	−0.988865	−	1.01101i	−0.0448558	−	0.0458605i
$487$		−	3.76034i		−	0.170397i	−0.996364	−	0.0851987i	$-0.972847\pi$
$487$		−	3.76034i		−	0.170397i	0.996364	−	0.0851987i	$-0.0271525\pi$
$488$	−17.6142	−	18.8252i	−0.797356	−	0.852178i
$489$			5.65996i			0.255952i
$490$		0			0
$491$			8.60497i			0.388337i	0.980968	+	0.194168i	$0.0622008\pi$
$491$			8.60497i			0.388337i	−0.980968	+	0.194168i	$0.937799\pi$
$492$	0.298374	+	0.00660954i	0.0134517	+	0.000297981i
$493$			33.9839i			1.53056i
$494$	−34.6919	+	33.9319i	−1.56086	+	1.52667i
$495$	−1.52397			−0.0684973
$496$	11.6774	+	0.517606i	0.524330	+	0.0232412i
$497$		0			0
$498$	−9.02763	−	9.22982i	−0.404538	−	0.413598i
$499$			18.5825i			0.831865i	0.909395	+	0.415933i	$0.136545\pi$
$499$			18.5825i			0.831865i	−0.909395	+	0.415933i	$0.863455\pi$
$500$	−19.6953	−	0.436289i	−0.880802	−	0.0195114i
$501$	4.84357			0.216395
$502$	1.66836	+	1.70573i	0.0744625	+	0.0761303i
$503$	−33.4544			−1.49166			−0.745828	−	0.666139i	$-0.767946\pi$
$503$	−33.4544			−1.49166			−0.745828	+	0.666139i	$0.767946\pi$
$504$		0			0
$505$	−0.897402			−0.0399338
$506$	8.82942	+	9.02718i	0.392516	+	0.401307i
$507$	−18.1910			−0.807891
$508$	−7.04715	−	0.156108i	−0.312667	−	0.00692616i
$509$		−	23.9925i		−	1.06345i	−0.846917	−	0.531725i	$-0.821544\pi$
$509$		−	23.9925i		−	1.06345i	0.846917	−	0.531725i	$-0.178456\pi$
$510$	4.43556	+	4.53490i	0.196410	+	0.200809i
$511$		0			0
$512$	−14.3286	−	17.5126i	−0.633239	−	0.773956i
$513$	6.14408			0.271268
$514$	21.5519	−	21.0797i	0.950612	−	0.929787i
$515$			3.78706i			0.166878i
$516$	−21.3062	−	0.471973i	−0.937954	−	0.0207775i
$517$		−	4.85315i		−	0.213441i
$518$		0			0
$519$		−	2.10368i		−	0.0923415i
$520$	13.0210	−	12.1834i	0.571010	−	0.534276i
$521$		−	14.0811i		−	0.616904i	−0.951240	−	0.308452i	$-0.900189\pi$
$521$		−	14.0811i		−	0.616904i	0.951240	−	0.308452i	$-0.0998109\pi$
$522$	−8.45746	−	8.64689i	−0.370173	−	0.378464i
$523$	35.1452			1.53679			0.768396	−	0.639975i	$-0.221055\pi$
$523$	35.1452			1.53679			0.768396	+	0.639975i	$0.221055\pi$
$524$	0.105062	−	4.74282i	0.00458967	−	0.207191i
$525$		0			0
$526$	−11.7122	+	11.4556i	−0.510675	+	0.499488i
$527$		−	11.6113i		−	0.505798i
$528$	0.239124	−	5.39472i	0.0104065	−	0.234775i
$529$	−20.7443			−0.901924
$530$	0.837239	−	0.818898i	0.0363673	−	0.0355706i
$531$	−14.4054			−0.625141
$532$		0			0
$533$	−0.833397			−0.0360984
$534$	−8.01476	+	7.83919i	−0.346833	+	0.339235i
$535$	−14.1684			−0.612551
$536$	−0.452375	−	0.483478i	−0.0195396	−	0.0208831i
$537$		−	4.00769i		−	0.172944i
$538$	−7.33338	+	7.17273i	−0.316164	+	0.309238i
$539$		0			0
$540$	−2.25717	−	0.0500006i	−0.0971332	−	0.00215168i
$541$	12.7152			0.546669			0.273334	−	0.961919i	$-0.411873\pi$
$541$	12.7152			0.546669			0.273334	+	0.961919i	$0.411873\pi$
$542$	28.6913	+	29.3339i	1.23240	+	1.26000i
$543$		−	5.89663i		−	0.253049i
$544$	−16.7491	+	14.9899i	−0.718114	+	0.642688i
$545$		−	17.2188i		−	0.737571i
$546$		0			0
$547$			42.0999i			1.80006i	0.435828	+	0.900030i	$0.356456\pi$
$547$			42.0999i			1.80006i	−0.435828	+	0.900030i	$0.643544\pi$
$548$	0.317829	−	14.3477i	0.0135770	−	0.612903i
$549$		−	9.11488i		−	0.389014i
$550$	5.08506	−	4.97366i	0.216827	−	0.212078i
$551$	52.5485			2.23864
$552$	12.7812	+	13.6600i	0.544004	+	0.581407i
$553$		0			0
$554$	0.341298	+	0.348942i	0.0145003	+	0.0148251i
$555$			7.14002i			0.303077i
$556$	1.00052	−	45.1665i	0.0424316	−	1.91548i
$557$	15.8853			0.673080			0.336540	−	0.941669i	$-0.390743\pi$
$557$	15.8853			0.673080			0.336540	+	0.941669i	$0.390743\pi$
$558$	2.88967	+	2.95439i	0.122330	+	0.125069i
$559$	59.5110			2.51705
$560$		0			0
$561$	−5.36420			−0.226477
$562$	−6.55354	−	6.70032i	−0.276444	−	0.282636i
$563$	−32.9188			−1.38736			−0.693681	−	0.720283i	$-0.744012\pi$
$563$	−32.9188			−1.38736			−0.693681	+	0.720283i	$0.744012\pi$
$564$	0.159229	−	7.18808i	0.00670477	−	0.302673i
$565$		−	13.2961i		−	0.559370i
$566$	27.4719	+	28.0872i	1.15473	+	1.18059i
$567$		0			0
$568$	−16.8917	−	18.0531i	−0.708762	−	0.757492i
$569$	34.9841			1.46661			0.733304	−	0.679901i	$-0.237977\pi$
$569$	34.9841			1.46661			0.733304	+	0.679901i	$0.237977\pi$
$570$	7.01221	−	6.85859i	0.293709	−	0.287275i
$571$		−	6.50173i		−	0.272089i	−0.990703	−	0.136044i	$-0.956561\pi$
$571$		−	6.50173i		−	0.272089i	0.990703	−	0.136044i	$-0.0434390\pi$
$572$	−0.333952	+	15.0755i	−0.0139632	+	0.630340i
$573$		−	25.3919i		−	1.06076i
$574$		0			0
$575$			24.6414i			1.02762i
$576$	0.531167	−	7.98235i	0.0221320	−	0.332598i
$577$			37.2134i			1.54921i	0.632444	+	0.774606i	$0.282052\pi$
$577$			37.2134i			1.54921i	−0.632444	+	0.774606i	$0.717948\pi$
$578$	−1.19801	−	1.22484i	−0.0498306	−	0.0509467i
$579$	0.0733869			0.00304986
$580$	−19.3049	−	0.427640i	−0.801593	−	0.0177568i
$581$		0			0
$582$	−6.29924	+	6.16125i	−0.261112	+	0.255392i
$583$			0.990345i			0.0410159i
$584$	−3.41168	−	3.64625i	−0.141176	−	0.150883i
$585$	6.30457			0.260662
$586$	7.36513	−	7.20379i	0.304251	−	0.297586i
$587$	24.7914			1.02325			0.511625	−	0.859209i	$-0.329044\pi$
$587$	24.7914			1.02325			0.511625	+	0.859209i	$0.329044\pi$
$588$		0			0
$589$	−17.9543			−0.739794
$590$	−16.4408	+	16.0806i	−0.676857	+	0.662029i
$591$	7.23506			0.297611
$592$	−25.2751	−	1.12033i	−1.03880	−	0.0460453i
$593$		−	31.0027i		−	1.27313i	−0.771223	−	0.636565i	$-0.780355\pi$
$593$		−	31.0027i		−	1.27313i	0.771223	−	0.636565i	$-0.219645\pi$
$594$	1.36487	−	1.33497i	0.0560013	−	0.0547745i
$595$		0			0
$596$	0.489465	−	22.0959i	0.0200493	−	0.905082i
$597$	15.3120			0.626677
$598$	−36.5268	−	37.3449i	−1.49369	−	1.52715i
$599$		−	8.22986i		−	0.336263i	−0.985765	−	0.168131i	$-0.946227\pi$
$599$		−	8.22986i		−	0.336263i	0.985765	−	0.168131i	$-0.0537733\pi$
$600$	7.69473	−	7.19972i	0.314136	−	0.293927i
$601$			47.6805i			1.94493i	0.233053	+	0.972464i	$0.425128\pi$
$601$			47.6805i			1.94493i	−0.233053	+	0.972464i	$0.574872\pi$
$602$		0			0
$603$		−	0.234093i		−	0.00953299i
$604$	−3.07824	−	0.0681889i	−0.125252	−	0.00277457i
$605$			10.3601i			0.421199i
$606$	0.803715	−	0.786109i	0.0326487	−	0.0319335i
$607$	−12.6543			−0.513621			−0.256810	−	0.966462i	$-0.582672\pi$
$607$	−12.6543			−0.513621			−0.256810	+	0.966462i	$0.582672\pi$
$608$	23.1786	+	25.8988i	0.940015	+	1.05033i
$609$		0			0
$610$	−10.1749	−	10.4028i	−0.411969	−	0.421196i
$611$			20.0772i			0.812238i
$612$	−7.94500	−	0.175997i	−0.321158	−	0.00711425i
$613$	0.452915			0.0182930			0.00914652	−	0.999958i	$-0.497089\pi$
$613$	0.452915			0.0182930			0.00914652	+	0.999958i	$0.497089\pi$
$614$	−26.8883	−	27.4905i	−1.08512	−	1.10943i
$615$	0.168453			0.00679267
$616$		0			0
$617$	−0.575345			−0.0231625			−0.0115813	−	0.999933i	$-0.503687\pi$
$617$	−0.575345			−0.0231625			−0.0115813	+	0.999933i	$0.503687\pi$
$618$	−3.31740	−	3.39170i	−0.133445	−	0.136434i
$619$	2.04323			0.0821243			0.0410622	−	0.999157i	$-0.486926\pi$
$619$	2.04323			0.0821243			0.0410622	+	0.999157i	$0.486926\pi$
$620$	6.59593	+	0.146112i	0.264899	+	0.00586801i
$621$			6.61394i			0.265408i
$622$	−20.6888	−	21.1522i	−0.829545	−	0.848125i
$623$		0			0
$624$	−0.989242	+	22.3177i	−0.0396014	+	0.893421i
$625$	7.50896			0.300358
$626$	−2.64624	+	2.58827i	−0.105765	+	0.103448i
$627$			8.29453i			0.331252i
$628$	17.1148	+	0.379124i	0.682953	+	0.0151287i
$629$			25.1321i			1.00208i
$630$		0			0
$631$		−	38.8983i		−	1.54852i	−0.632870	−	0.774258i	$-0.718123\pi$
$631$		−	38.8983i		−	1.54852i	0.632870	−	0.774258i	$-0.281877\pi$
$632$	−16.2476	−	17.3647i	−0.646295	−	0.690730i
$633$			13.7540i			0.546670i
$634$	12.8044	+	13.0912i	0.508529	+	0.519918i
$635$	−3.97861			−0.157886
$636$	−0.0324927	+	1.46681i	−0.00128842	+	0.0581630i
$637$		0			0
$638$	11.6733	−	11.4176i	0.462151	−	0.452027i
$639$		−	8.74104i		−	0.345790i
$640$	−8.30442	−	9.70315i	−0.328261	−	0.383551i
$641$	−2.06073			−0.0813938			−0.0406969	−	0.999172i	$-0.512958\pi$
$641$	−2.06073			−0.0813938			−0.0406969	+	0.999172i	$0.512958\pi$
$642$	12.6892	−	12.4112i	0.500803	−	0.489833i
$643$	−2.86029			−0.112799			−0.0563994	−	0.998408i	$-0.517962\pi$
$643$	−2.86029			−0.112799			−0.0563994	+	0.998408i	$0.517962\pi$
$644$		0			0
$645$	−12.0288			−0.473635
$646$	24.6822	−	24.1415i	0.971109	−	0.949835i
$647$	−19.4084			−0.763021			−0.381511	−	0.924364i	$-0.624596\pi$
$647$	−19.4084			−0.763021			−0.381511	+	0.924364i	$0.624596\pi$
$648$	2.06533	−	1.93246i	0.0811338	−	0.0759143i
$649$		−	19.4473i		−	0.763375i
$650$	−21.0366	+	20.5758i	−0.825123	+	0.807048i
$651$		0			0
$652$	−11.3171	−	0.250696i	−0.443214	−	0.00981802i
$653$	−0.729729			−0.0285565			−0.0142783	−	0.999898i	$-0.504545\pi$
$653$	−0.729729			−0.0285565			−0.0142783	+	0.999898i	$0.504545\pi$
$654$	15.0833	+	15.4212i	0.589806	+	0.603016i
$655$		−	2.67765i		−	0.104625i
$656$	−0.0264317	+	0.596308i	−0.00103198	+	0.0232819i
$657$		−	1.76546i		−	0.0688771i
$658$		0			0
$659$			19.6921i			0.767097i	0.923521	+	0.383548i	$0.125298\pi$
$659$			19.6921i			0.767097i	−0.923521	+	0.383548i	$0.874702\pi$
$660$	0.0675010	−	3.04719i	0.00262747	−	0.118612i
$661$		−	9.40545i		−	0.365830i	−0.983129	−	0.182915i	$-0.941447\pi$
$661$		−	9.40545i		−	0.365830i	0.983129	−	0.182915i	$-0.0585533\pi$
$662$	5.29769	−	5.18164i	0.205901	−	0.201390i
$663$	22.1914			0.861843
$664$	18.8550	−	17.6420i	0.731715	−	0.684643i
$665$		0			0
$666$	−6.25454	−	6.39463i	−0.242359	−	0.247787i
$667$			56.5671i			2.19029i
$668$	−0.214536	+	9.68476i	−0.00830064	+	0.374715i
$669$	−16.4120			−0.634526
$670$	−0.261316	−	0.267169i	−0.0100955	−	0.0103216i
$671$	12.3051			0.475034
$672$		0			0
$673$	30.0031			1.15653			0.578266	−	0.815848i	$-0.303729\pi$
$673$	30.0031			1.15653			0.578266	+	0.815848i	$0.303729\pi$
$674$	−21.4423	−	21.9225i	−0.825925	−	0.844424i
$675$	3.72567			0.143401
$676$	0.805733	−	36.3731i	0.0309897	−	1.39897i
$677$			30.8100i			1.18413i	0.805892	+	0.592063i	$0.201686\pi$
$677$			30.8100i			1.18413i	−0.805892	+	0.592063i	$0.798314\pi$
$678$	11.6471	+	11.9080i	0.447305	+	0.457324i
$679$		0			0
$680$	−9.26405	+	8.66808i	−0.355260	+	0.332406i
$681$	16.1319			0.618176
$682$	−3.98844	+	3.90107i	−0.152725	+	0.149380i
$683$		−	41.6279i		−	1.59285i	−0.604739	−	0.796424i	$-0.706722\pi$
$683$		−	41.6279i		−	1.59285i	0.604739	−	0.796424i	$-0.293278\pi$
$684$	−0.272139	+	12.2852i	−0.0104055	+	0.469735i
$685$		−	8.10028i		−	0.309496i
$686$		0			0
$687$			21.6682i			0.826693i
$688$	1.88743	−	42.5811i	0.0719575	−	1.62339i
$689$		−	4.09700i		−	0.156083i
$690$	7.38310	+	7.54846i	0.281070	+	0.287365i
$691$	−8.78828			−0.334322			−0.167161	−	0.985930i	$-0.553460\pi$
$691$	−8.78828			−0.334322			−0.167161	+	0.985930i	$0.553460\pi$
$692$	4.20634	+	0.0931783i	0.159901	+	0.00354211i
$693$		0			0
$694$	−0.662831	+	0.648311i	−0.0251607	+	0.0246095i
$695$		−	25.4996i		−	0.967256i
$696$	17.6641	−	16.5278i	0.669557	−	0.626484i
$697$	0.592936			0.0224590
$698$	−19.6295	+	19.1995i	−0.742987	+	0.726711i
$699$	−19.0312			−0.719827
$700$		0			0
$701$	−0.0621184			−0.00234618			−0.00117309	−	0.999999i	$-0.500373\pi$
$701$	−0.0621184			−0.00234618			−0.00117309	+	0.999999i	$0.500373\pi$
$702$	−5.64640	+	5.52270i	−0.213109	+	0.208441i
$703$	38.8612			1.46568
$704$	10.7762	+	0.717078i	0.406143	+	0.0270259i
$705$		−	4.05817i		−	0.152840i
$706$	−30.2135	+	29.5516i	−1.13710	+	1.11219i
$707$		0			0
$708$	0.638057	−	28.8037i	0.0239797	−	1.08251i
$709$	33.2035			1.24698			0.623492	−	0.781830i	$-0.285713\pi$
$709$	33.2035			1.24698			0.623492	+	0.781830i	$0.285713\pi$
$710$	−9.75756	−	9.97610i	−0.366195	−	0.374396i
$711$		−	8.40771i		−	0.315314i
$712$	−15.3195	−	16.3728i	−0.574124	−	0.613597i
$713$		−	19.3273i		−	0.723815i
$714$		0			0
$715$			8.51120i			0.318301i
$716$	8.01341	+	0.177512i	0.299475	+	0.00663394i
$717$		−	15.6878i		−	0.585873i
$718$	−12.7320	+	12.4531i	−0.475154	+	0.464745i
$719$	−31.9070			−1.18993			−0.594966	−	0.803751i	$-0.702834\pi$
$719$	−31.9070			−1.18993			−0.594966	+	0.803751i	$0.702834\pi$
$720$	0.199953	−	4.51102i	0.00745182	−	0.168116i
$721$		0			0
$722$	−18.5410	−	18.9562i	−0.690024	−	0.705478i
$723$		−	11.9011i		−	0.442605i
$724$	11.7904	+	0.261179i	0.438185	+	0.00970663i
$725$	31.8645			1.18342
$726$	−9.07530	−	9.27856i	−0.336816	−	0.344360i
$727$	−11.8242			−0.438535			−0.219268	−	0.975665i	$-0.570367\pi$
$727$	−11.8242			−0.438535			−0.219268	+	0.975665i	$0.570367\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−1.97077	−	2.01491i	−0.0729414	−	0.0745751i
$731$	−42.3402			−1.56601
$732$	18.2253	+	0.403725i	0.673626	+	0.0149221i
$733$			11.8182i			0.436515i	0.975891	+	0.218258i	$0.0700373\pi$
$733$			11.8182i			0.436515i	−0.975891	+	0.218258i	$0.929963\pi$
$734$	−5.40803	−	5.52915i	−0.199614	−	0.204085i
$735$		0			0
$736$	−27.8794	+	24.9511i	−1.02765	+	0.919710i
$737$	0.316026			0.0116410
$738$	−0.150867	+	0.147562i	−0.00555348	+	0.00543183i
$739$		−	26.5948i		−	0.978305i	−0.872198	−	0.489153i	$-0.837306\pi$
$739$		−	26.5948i		−	0.978305i	0.872198	−	0.489153i	$-0.162694\pi$
$740$	−14.2765	−	0.316253i	−0.524816	−	0.0116257i
$741$		−	34.3140i		−	1.26056i
$742$		0			0
$743$		−	34.9119i		−	1.28079i	−0.768045	−	0.640396i	$-0.778770\pi$
$743$		−	34.9119i		−	1.28079i	0.768045	−	0.640396i	$-0.221230\pi$
$744$	−6.03533	+	5.64707i	−0.221266	+	0.207032i
$745$		−	12.4747i		−	0.457036i
$746$	14.6828	+	15.0116i	0.537574	+	0.549614i
$747$	9.12928			0.334023
$748$	0.237596	−	10.7258i	0.00868738	−	0.392173i
$749$		0			0
$750$	9.95856	−	9.74040i	0.363635	−	0.355669i
$751$		−	1.72010i		−	0.0627672i	−0.999507	−	0.0313836i	$-0.990009\pi$
$751$		−	1.72010i		−	0.0627672i	0.999507	−	0.0313836i	$-0.00999135\pi$
$752$	14.3656	+	0.636762i	0.523859	+	0.0232203i
$753$	−1.68715			−0.0614830
$754$	−48.2919	+	47.2340i	−1.75869	+	1.72016i
$755$	−1.73788			−0.0632480
$756$		0			0
$757$	33.2057			1.20688			0.603440	−	0.797408i	$-0.293796\pi$
$757$	33.2057			1.20688			0.603440	+	0.797408i	$0.293796\pi$
$758$	−30.9507	+	30.2727i	−1.12418	+	1.09955i
$759$	−8.92885			−0.324097
$760$	13.4032	+	14.3248i	0.486186	+	0.519614i
$761$		−	27.1774i		−	0.985180i	−0.870262	−	0.492590i	$-0.836050\pi$
$761$		−	27.1774i		−	0.985180i	0.870262	−	0.492590i	$-0.163950\pi$
$762$	3.56325	−	3.48519i	0.129083	−	0.126255i
$763$		0			0
$764$	50.7713	+	1.12468i	1.83684	+	0.0406895i
$765$	−4.48551			−0.162174
$766$	23.2169	+	23.7369i	0.838862	+	0.857650i
$767$			80.4526i			2.90497i
$768$	15.9373	+	1.41564i	0.575086	+	0.0510824i
$769$			7.13960i			0.257460i	0.991680	+	0.128730i	$0.0410901\pi$
$769$			7.13960i			0.257460i	−0.991680	+	0.128730i	$0.958910\pi$
$770$		0			0
$771$			21.3171i			0.767717i
$772$	−0.00325052	+	0.146738i	−0.000116989	+	0.00528121i
$773$			26.5575i			0.955207i	0.878575	+	0.477604i	$0.158494\pi$
$773$			26.5575i			0.955207i	−0.878575	+	0.477604i	$0.841506\pi$
$774$	10.7731	−	10.5371i	0.387230	−	0.378747i
$775$	−10.8872			−0.391079
$776$	−12.0405	−	12.8683i	−0.432227	−	0.461945i
$777$		0			0
$778$	35.7746	+	36.5758i	1.28258	+	1.31131i
$779$		−	0.916841i		−	0.0328492i
$780$	−0.279248	+	12.6061i	−0.00999868	+	0.451369i
$781$	11.8004			0.422253
$782$	25.9877	+	26.5698i	0.929318	+	0.950132i
$783$	8.55270			0.305648
$784$		0			0
$785$	9.66247			0.344869
$786$	2.34558	+	2.39811i	0.0836640	+	0.0855379i
$787$	24.4670			0.872153			0.436077	−	0.899910i	$-0.356368\pi$
$787$	24.4670			0.872153			0.436077	+	0.899910i	$0.356368\pi$
$788$	−0.320462	+	14.4666i	−0.0114160	+	0.515351i
$789$		−	11.5846i		−	0.412423i
$790$	−9.38546	−	9.59567i	−0.333920	−	0.341399i
$791$		0			0
$792$	2.60883	+	2.78820i	0.0927008	+	0.0990744i
$793$	−50.9056			−1.80771
$794$	−1.34640	+	1.31691i	−0.0477820	+	0.0467353i
$795$			0.828119i			0.0293704i
$796$	−0.678211	+	30.6164i	−0.0240386	+	1.08517i
$797$		−	26.0084i		−	0.921265i	−0.887591	−	0.460632i	$-0.847623\pi$
$797$		−	26.0084i		−	0.921265i	0.887591	−	0.460632i	$-0.152377\pi$
$798$		0			0
$799$		−	14.2843i		−	0.505343i
$800$	14.0551	+	15.7046i	0.496922	+	0.555241i
$801$		−	7.92746i		−	0.280103i
$802$	−25.7694	−	26.3466i	−0.909950	−	0.930330i
$803$	2.38337			0.0841075
$804$	0.468070	+	0.0103686i	0.0165076	+	0.000365674i
$805$		0			0
$806$	16.5000	−	16.1385i	0.581186	−	0.568454i
$807$		−	7.25350i		−	0.255335i
$808$	1.53623	+	1.64186i	0.0540445	+	0.0577603i
$809$	−13.1975			−0.464001			−0.232000	−	0.972716i	$-0.574527\pi$
$809$	−13.1975			−0.464001			−0.232000	+	0.972716i	$0.574527\pi$
$810$	1.14129	−	1.11629i	0.0401010	−	0.0392225i
$811$	4.87597			0.171219			0.0856093	−	0.996329i	$-0.472716\pi$
$811$	4.87597			0.171219			0.0856093	+	0.996329i	$0.472716\pi$
$812$		0			0
$813$	−29.0144			−1.01758
$814$	8.63277	−	8.44365i	0.302578	−	0.295950i
$815$	−6.38932			−0.223808
$816$	0.703814	−	15.8783i	0.0246384	−	0.555852i
$817$			65.4696i			2.29049i
$818$	13.4676	−	13.1725i	0.470883	−	0.460567i
$819$		0			0
$820$	−0.00746126	+	0.336823i	−0.000260559	+	0.0117624i
$821$	7.06581			0.246599			0.123299	−	0.992370i	$-0.460652\pi$
$821$	7.06581			0.246599			0.123299	+	0.992370i	$0.460652\pi$
$822$	7.09571	+	7.25463i	0.247491	+	0.253034i
$823$		−	21.9614i		−	0.765528i	−0.923846	−	0.382764i	$-0.874972\pi$
$823$		−	21.9614i		−	0.765528i	0.923846	−	0.382764i	$-0.125028\pi$
$824$	6.92868	−	6.48295i	0.241372	−	0.225844i
$825$			5.02967i			0.175110i
$826$		0			0
$827$		−	17.4897i		−	0.608175i	−0.952644	−	0.304088i	$-0.901648\pi$
$827$		−	17.4897i		−	0.608175i	0.952644	−	0.304088i	$-0.0983515\pi$
$828$	−13.2246	−	0.292951i	−0.459588	−	0.0101807i
$829$			25.6021i			0.889199i	0.895730	+	0.444599i	$0.146654\pi$
$829$			25.6021i			0.889199i	−0.895730	+	0.444599i	$0.853346\pi$
$830$	10.4192	−	10.1910i	0.361656	−	0.353733i
$831$	−0.345141			−0.0119728
$832$	−44.5805	−	2.96651i	−1.54555	−	0.102845i
$833$		0			0
$834$	22.3372	+	22.8375i	0.773475	+	0.790799i
$835$			5.46772i			0.189218i
$836$	−16.5850	−	0.367389i	−0.573604	−	0.0127064i
$837$	−2.92221			−0.101006
$838$	7.46260	+	7.62974i	0.257791	+	0.263565i
$839$	−9.04513			−0.312273			−0.156136	−	0.987736i	$-0.549904\pi$
$839$	−9.04513			−0.312273			−0.156136	+	0.987736i	$0.549904\pi$
$840$		0			0
$841$	44.1486			1.52237
$842$	−2.64086	−	2.70001i	−0.0910100	−	0.0930484i
$843$	6.62734			0.228258
$844$	−27.5012	−	0.609203i	−0.946629	−	0.0209696i
$845$		−	20.5351i		−	0.706431i
$846$	3.55489	+	3.63451i	0.122220	+	0.124957i
$847$		0			0
$848$	−2.93147	−	0.129939i	−0.100667	−	0.00446212i
$849$	−27.7813			−0.953452
$850$	14.9669	−	14.6390i	0.513360	−	0.502114i
$851$			41.8330i			1.43402i
$852$	17.4778	+	0.387166i	0.598779	+	0.0132641i
$853$			28.8642i			0.988292i	0.869379	+	0.494146i	$0.164519\pi$
$853$			28.8642i			0.988292i	−0.869379	+	0.494146i	$0.835481\pi$
$854$		0			0
$855$			6.93583i			0.237200i
$856$	24.2543	+	25.9219i	0.828997	+	0.885994i
$857$		−	48.3887i		−	1.65293i	−0.562992	−	0.826463i	$-0.690350\pi$
$857$		−	48.3887i		−	1.65293i	0.562992	−	0.826463i	$-0.309650\pi$
$858$	−7.45567	−	7.62265i	−0.254532	−	0.260233i
$859$	19.8378			0.676858			0.338429	−	0.940992i	$-0.390104\pi$
$859$	19.8378			0.676858			0.338429	+	0.940992i	$0.390104\pi$
$860$	0.532793	−	24.0518i	0.0181681	−	0.820159i
$861$		0			0
$862$	−12.0171	+	11.7539i	−0.409304	+	0.400338i
$863$			38.7992i			1.32074i	0.750940	+	0.660370i	$0.229601\pi$
$863$			38.7992i			1.32074i	−0.750940	+	0.660370i	$0.770399\pi$
$864$	3.77250	+	4.21524i	0.128343	+	0.143405i
$865$	2.37477			0.0807446
$866$	20.8943	−	20.4365i	0.710016	−	0.694462i
$867$	1.21150			0.0411447
$868$		0			0
$869$	11.3504			0.385037
$870$	9.76115	−	9.54731i	0.330934	−	0.323684i
$871$	−1.30738			−0.0442989
$872$	−31.5029	+	29.4763i	−1.06682	+	0.998192i
$873$		−	6.23063i		−	0.210875i
$874$	41.0841	−	40.1841i	1.38969	−	1.35925i
$875$		0			0
$876$	3.53005	+	0.0781973i	0.119269	+	0.00264204i
$877$	−14.9697			−0.505492			−0.252746	−	0.967533i	$-0.581334\pi$
$877$	−14.9697			−0.505492			−0.252746	+	0.967533i	$0.581334\pi$
$878$	−5.36028	−	5.48033i	−0.180901	−	0.184952i
$879$			7.28491i			0.245714i
$880$	6.08989	+	0.269938i	0.205290	+	0.00909960i
$881$		−	44.9991i		−	1.51606i	−0.652221	−	0.758029i	$-0.726163\pi$
$881$		−	44.9991i		−	1.51606i	0.652221	−	0.758029i	$-0.273837\pi$
$882$		0			0
$883$		−	20.0940i		−	0.676217i	−0.941107	−	0.338109i	$-0.890213\pi$
$883$		−	20.0940i		−	0.676217i	0.941107	−	0.338109i	$-0.109787\pi$
$884$	−0.982923	+	44.3720i	−0.0330593	+	1.49239i
$885$		−	16.2617i		−	0.546632i
$886$	22.9538	−	22.4510i	0.771148	−	0.754255i
$887$	−15.2147			−0.510859			−0.255430	−	0.966828i	$-0.582217\pi$
$887$	−15.2147			−0.510859			−0.255430	+	0.966828i	$0.582217\pi$
$888$	13.0631	−	12.2228i	0.438371	−	0.410170i
$889$		0			0
$890$	−8.84937	−	9.04757i	−0.296631	−	0.303275i
$891$			1.35000i			0.0452268i
$892$	0.726937	−	32.8160i	0.0243396	−	1.09876i
$893$	−22.0875			−0.739130
$894$	10.9276	+	11.1723i	0.365473	+	0.373659i
$895$	4.52413			0.151225
$896$		0			0
$897$	36.9382			1.23333
$898$	15.4773	+	15.8240i	0.516485	+	0.528052i
$899$	−24.9928			−0.833556
$900$	−0.165021	+	7.44951i	−0.00550069	+	0.248317i
$901$			2.91489i			0.0971090i
$902$	−0.199209	−	0.203671i	−0.00663293	−	0.00678149i
$903$		0			0
$904$	−24.3260	+	22.7611i	−0.809072	+	0.757023i
$905$	6.65648			0.221269
$906$	1.55645	−	1.52236i	0.0517097	−	0.0505769i
$907$		−	14.1218i		−	0.468906i	−0.972127	−	0.234453i	$-0.924670\pi$
$907$		−	14.1218i		−	0.468906i	0.972127	−	0.234453i	$-0.0753298\pi$
$908$	−0.714529	+	32.2559i	−0.0237125	+	1.07045i
$909$			0.794961i			0.0263672i
$910$		0			0
$911$		−	12.5510i		−	0.415832i	−0.978147	−	0.207916i	$-0.933332\pi$
$911$		−	12.5510i		−	0.415832i	0.978147	−	0.207916i	$-0.0666681\pi$
$912$	−24.5522	−	1.08829i	−0.813005	−	0.0360369i
$913$			12.3246i			0.407884i
$914$	16.8370	+	17.2141i	0.556918	+	0.569391i
$915$	10.2894			0.340159
$916$	−43.3257	−	0.959747i	−1.43152	−	0.0317109i
$917$		0			0
$918$	4.01723	−	3.92923i	0.132588	−	0.129684i
$919$			35.4545i			1.16954i	0.811201	+	0.584768i	$0.198814\pi$
$919$			35.4545i			1.16954i	−0.811201	+	0.584768i	$0.801186\pi$
$920$	−15.4202	+	14.4282i	−0.508390	+	0.475685i
$921$	27.1911			0.895977
$922$	38.5287	−	37.6847i	1.26887	−	1.24108i
$923$	−48.8178			−1.60686
$924$		0			0
$925$	23.5648			0.774804
$926$	1.40488	−	1.37411i	0.0461674	−	0.0451560i
$927$	3.35476			0.110185
$928$	32.2651	+	36.0517i	1.05915	+	1.18345i
$929$			55.5048i			1.82105i	0.413451	+	0.910526i	$0.364323\pi$
$929$			55.5048i			1.82105i	−0.413451	+	0.910526i	$0.635677\pi$
$930$	−3.33510	+	3.26204i	−0.109362	+	0.106967i
$931$		0			0
$932$	0.842949	−	38.0531i	0.0276117	−	1.24647i
$933$	20.9218			0.684948
$934$	3.45491	+	3.53229i	0.113048	+	0.115580i
$935$		−	6.05545i		−	0.198034i
$936$	−10.7926	−	11.5346i	−0.352767	−	0.377021i
$937$		−	18.8683i		−	0.616400i	−0.951322	−	0.308200i	$-0.900273\pi$
$937$		−	18.8683i		−	0.616400i	0.951322	−	0.308200i	$-0.0997265\pi$
$938$		0			0
$939$		−	2.61741i		−	0.0854160i
$940$	8.11435	+	0.179748i	0.264661	+	0.00586274i
$941$		−	40.2290i		−	1.31143i	−0.755009	−	0.655715i	$-0.772367\pi$
$941$		−	40.2290i		−	1.31143i	0.755009	−	0.655715i	$-0.227633\pi$
$942$	−8.65374	+	8.46417i	−0.281954	+	0.275777i
$943$	0.986956			0.0321397
$944$	57.5651	+	2.55160i	1.87358	+	0.0830476i
$945$		0			0
$946$	14.2251	+	14.5437i	0.462497	+	0.472856i
$947$		−	49.5808i		−	1.61116i	−0.592488	−	0.805579i	$-0.701854\pi$
$947$		−	49.5808i		−	1.61116i	0.592488	−	0.805579i	$-0.298146\pi$
$948$	16.8113	+	0.372402i	0.546005	+	0.0120951i
$949$	−9.85989			−0.320066
$950$	−22.6359	−	23.1429i	−0.734406	−	0.750855i
$951$	−12.9486			−0.419887
$952$		0			0
$953$	−35.9273			−1.16380			−0.581900	−	0.813260i	$-0.697691\pi$
$953$	−35.9273			−1.16380			−0.581900	+	0.813260i	$0.697691\pi$
$954$	−0.725418	−	0.741666i	−0.0234863	−	0.0240123i
$955$	28.6639			0.927543
$956$	31.3680	+	0.694860i	1.01451	+	0.0224734i
$957$			11.5462i			0.373235i
$958$	−13.5688	−	13.8727i	−0.438388	−	0.448206i
$959$		0			0
$960$	9.01097	+	0.599615i	0.290828	+	0.0193525i
$961$	−22.4607			−0.724538
$962$	−35.7133	+	34.9309i	−1.15144	+	1.12622i
$963$			12.5510i			0.404450i
$964$	23.7963	+	0.527133i	0.766427	+	0.0169778i
$965$			0.0828437i			0.00266683i
$966$		0			0
$967$			33.5277i			1.07818i	0.842249	+	0.539089i	$0.181231\pi$
$967$			33.5277i			1.07818i	−0.842249	+	0.539089i	$0.818769\pi$
$968$	18.9545	−	17.7352i	0.609222	−	0.570030i
$969$			24.4134i			0.784270i
$970$	−6.95520	−	7.11098i	−0.223318	−	0.228320i
$971$	−14.7198			−0.472381			−0.236191	−	0.971707i	$-0.575899\pi$
$971$	−14.7198			−0.472381			−0.236191	+	0.971707i	$0.575899\pi$
$972$	−0.0442929	+	1.99951i	−0.00142070	+	0.0641343i
$973$		0			0
$974$	−3.80175	+	3.71847i	−0.121816	+	0.119148i
$975$		−	20.8075i		−	0.666372i
$976$	−1.61450	+	36.4238i	−0.0516790	+	1.16590i
$977$	−8.97289			−0.287068			−0.143534	−	0.989645i	$-0.545847\pi$
$977$	−8.97289			−0.287068			−0.143534	+	0.989645i	$0.545847\pi$
$978$	5.72229	−	5.59694i	0.182979	−	0.178970i
$979$	10.7021			0.342041
$980$		0			0
$981$	−15.2532			−0.486997
$982$	8.69973	−	8.50915i	0.277620	−	0.271538i
$983$	−1.86632			−0.0595265			−0.0297633	−	0.999557i	$-0.509475\pi$
$983$	−1.86632			−0.0595265			−0.0297633	+	0.999557i	$0.509475\pi$
$984$	−0.288369	−	0.308195i	−0.00919286	−	0.00982491i
$985$			8.16739i			0.260235i
$986$	34.3582	−	33.6055i	1.09419	−	1.07022i
$987$		0			0
$988$	68.6112	+	1.51987i	2.18281	+	0.0483535i
$989$	−70.4763			−2.24102
$990$	1.50700	+	1.54075i	0.0478956	+	0.0489683i
$991$			6.49237i			0.206237i	0.994669	+	0.103119i	$0.0328821\pi$
$991$			6.49237i			0.206237i	−0.994669	+	0.103119i	$0.967118\pi$
$992$	−11.0240	−	12.3178i	−0.350014	−	0.391091i
$993$			5.23999i			0.166286i
$994$		0			0
$995$			17.2851i			0.547974i
$996$	−0.404363	+	18.2541i	−0.0128127	+	0.578403i
$997$		−	12.3327i		−	0.390582i	−0.980745	−	0.195291i	$-0.937435\pi$
$997$		−	12.3327i		−	0.390582i	0.980745	−	0.195291i	$-0.0625651\pi$
$998$	18.7871	−	18.3755i	0.594695	−	0.581667i
$999$	6.32497			0.200113

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.b.d.391.1	yes	12
3.2	odd	2		1764.2.b.m.1567.12		12
4.3	odd	2		588.2.b.c.391.2	yes	12
7.2	even	3		588.2.o.e.31.6		24
7.3	odd	6		588.2.o.f.19.11		24
7.4	even	3		588.2.o.e.19.11		24
7.5	odd	6		588.2.o.f.31.6		24
7.6	odd	2		588.2.b.c.391.1	✓	12
12.11	even	2		1764.2.b.l.1567.11		12
21.20	even	2		1764.2.b.l.1567.12		12
28.3	even	6		588.2.o.e.19.6		24
28.11	odd	6		588.2.o.f.19.6		24
28.19	even	6		588.2.o.e.31.11		24
28.23	odd	6		588.2.o.f.31.11		24
28.27	even	2	inner	588.2.b.d.391.2	yes	12
84.83	odd	2		1764.2.b.m.1567.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.b.c.391.1	✓	12	7.6	odd	2
588.2.b.c.391.2	yes	12	4.3	odd	2
588.2.b.d.391.1	yes	12	1.1	even	1	trivial
588.2.b.d.391.2	yes	12	28.27	even	2	inner
588.2.o.e.19.6		24	28.3	even	6
588.2.o.e.19.11		24	7.4	even	3
588.2.o.e.31.6		24	7.2	even	3
588.2.o.e.31.11		24	28.19	even	6
588.2.o.f.19.6		24	28.11	odd	6
588.2.o.f.19.11		24	7.3	odd	6
588.2.o.f.31.6		24	7.5	odd	6
588.2.o.f.31.11		24	28.23	odd	6
1764.2.b.l.1567.11		12	12.11	even	2
1764.2.b.l.1567.12		12	21.20	even	2
1764.2.b.m.1567.11		12	84.83	odd	2
1764.2.b.m.1567.12		12	3.2	odd	2

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

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.988865 - 1.01101i) q^{2} +1.00000 q^{3} +(-0.0442929 + 1.99951i) q^{4} +1.12886i q^{5} +(-0.988865 - 1.01101i) q^{6} +(2.06533 - 1.93246i) q^{8} +1.00000 q^{9} +(1.14129 - 1.11629i) q^{10} +1.35000i q^{11} +(-0.0442929 + 1.99951i) q^{12} -5.58489i q^{13} +1.12886i q^{15} +(-3.99608 - 0.177128i) q^{16} +3.97347i q^{17} +(-0.988865 - 1.01101i) q^{18} +6.14408 q^{19} +(-2.25717 - 0.0500006i) q^{20} +(1.36487 - 1.33497i) q^{22} +6.61394i q^{23} +(2.06533 - 1.93246i) q^{24} +3.72567 q^{25} +(-5.64640 + 5.52270i) q^{26} +1.00000 q^{27} +8.55270 q^{29} +(1.14129 - 1.11629i) q^{30} -2.92221 q^{31} +(3.77250 + 4.21524i) q^{32} +1.35000i q^{33} +(4.01723 - 3.92923i) q^{34} +(-0.0442929 + 1.99951i) q^{36} +6.32497 q^{37} +(-6.07567 - 6.21175i) q^{38} -5.58489i q^{39} +(2.18149 + 2.33147i) q^{40} -0.149223i q^{41} +10.6557i q^{43} +(-2.69934 - 0.0597956i) q^{44} +1.12886i q^{45} +(6.68678 - 6.54030i) q^{46} -3.59492 q^{47} +(-3.99608 - 0.177128i) q^{48} +(-3.68418 - 3.76670i) q^{50} +3.97347i q^{51} +(11.1670 + 0.247371i) q^{52} +0.733587 q^{53} +(-0.988865 - 1.01101i) q^{54} -1.52397 q^{55} +6.14408 q^{57} +(-8.45746 - 8.64689i) q^{58} -14.4054 q^{59} +(-2.25717 - 0.0500006i) q^{60} -9.11488i q^{61} +(2.88967 + 2.95439i) q^{62} +(0.531167 - 7.98235i) q^{64} +6.30457 q^{65} +(1.36487 - 1.33497i) q^{66} -0.234093i q^{67} +(-7.94500 - 0.175997i) q^{68} +6.61394i q^{69} -8.74104i q^{71} +(2.06533 - 1.93246i) q^{72} -1.76546i q^{73} +(-6.25454 - 6.39463i) q^{74} +3.72567 q^{75} +(-0.272139 + 12.2852i) q^{76} +(-5.64640 + 5.52270i) q^{78} -8.40771i q^{79} +(0.199953 - 4.51102i) q^{80} +1.00000 q^{81} +(-0.150867 + 0.147562i) q^{82} +9.12928 q^{83} -4.48551 q^{85} +(10.7731 - 10.5371i) q^{86} +8.55270 q^{87} +(2.60883 + 2.78820i) q^{88} -7.92746i q^{89} +(1.14129 - 1.11629i) q^{90} +(-13.2246 - 0.292951i) q^{92} -2.92221 q^{93} +(3.55489 + 3.63451i) q^{94} +6.93583i q^{95} +(3.77250 + 4.21524i) q^{96} -6.23063i q^{97} +1.35000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 12 q^{3} - 4 q^{4} + 4 q^{6} + 4 q^{8} + 12 q^{9} - 4 q^{12} - 4 q^{16} + 4 q^{18} - 24 q^{20} + 4 q^{24} - 12 q^{25} + 24 q^{26} + 12 q^{27} + 32 q^{29} + 16 q^{31} + 4 q^{32} + 32 q^{34}+ \cdots + 4 q^{96}+O(q^{100}) \) 12 * q + 4 * q^2 + 12 * q^3 - 4 * q^4 + 4 * q^6 + 4 * q^8 + 12 * q^9 - 4 * q^12 - 4 * q^16 + 4 * q^18 - 24 * q^20 + 4 * q^24 - 12 * q^25 + 24 * q^26 + 12 * q^27 + 32 * q^29 + 16 * q^31 + 4 * q^32 + 32 * q^34 - 4 * q^36 + 32 * q^37 - 24 * q^38 - 32 * q^40 - 24 * q^44 + 24 * q^46 - 4 * q^48 - 28 * q^50 + 32 * q^52 - 32 * q^53 + 4 * q^54 + 16 * q^55 + 16 * q^58 - 16 * q^59 - 24 * q^60 + 8 * q^62 - 4 * q^64 - 8 * q^68 + 4 * q^72 - 32 * q^74 - 12 * q^75 - 32 * q^76 + 24 * q^78 - 16 * q^80 + 12 * q^81 + 32 * q^82 - 16 * q^83 + 16 * q^85 - 24 * q^86 + 32 * q^87 + 24 * q^88 + 16 * q^93 + 4 * q^96

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