LMFDB - Embedded newform 836.2.j.a.685.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [836,2,Mod(229,836)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(836, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("836.229"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 836 = 2^{2} \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	836.j (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.67549360898$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 9 x^{10} - 11 x^{9} + 52 x^{8} + 45 x^{7} + 155 x^{6} + 472 x^{5} + 1093 x^{4} + \cdots + 16 $ x^12 - x^11 + 9x^10 - 11x^9 + 52x^8 + 45x^7 + 155x^6 + 472x^5 + 1093x^4 + 778x^3 + 400x^2 + 112x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			685.1
Root			$-0.895600 + 2.75637i$ of defining polynomial
Character	$\chi$	$=$	836.685
Dual form			836.2.j.a.609.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.895600 - 2.75637i) q^{3} +(-1.97741 - 1.43667i) q^{5} +(-0.0757739 + 0.233208i) q^{7} +(-4.36844 + 3.17385i) q^{9} +(0.309017 + 3.30220i) q^{11} +(-3.79382 + 2.75637i) q^{13} +(-2.18903 + 6.73715i) q^{15} +(2.05975 + 1.49650i) q^{17} +(0.309017 + 0.951057i) q^{19} +0.710671 q^{21} +0.746673 q^{23} +(0.301033 + 0.926485i) q^{25} +(5.62656 + 4.08794i) q^{27} +(0.797879 - 2.45562i) q^{29} +(0.765599 - 0.556240i) q^{31} +(8.82533 - 3.80921i) q^{33} +(0.484879 - 0.352285i) q^{35} +(-0.123509 + 0.380122i) q^{37} +(10.9953 + 7.98857i) q^{39} +(-2.62478 - 8.07825i) q^{41} -8.39378 q^{43} +13.1980 q^{45} +(1.43142 + 4.40545i) q^{47} +(5.61447 + 4.07915i) q^{49} +(2.28019 - 7.01769i) q^{51} +(-6.27695 + 4.56047i) q^{53} +(4.13312 - 6.97375i) q^{55} +(2.34471 - 1.70353i) q^{57} +(-3.92228 + 12.0715i) q^{59} +(3.33307 + 2.42162i) q^{61} +(-0.409155 - 1.25925i) q^{63} +11.4619 q^{65} -12.4465 q^{67} +(-0.668720 - 2.05811i) q^{69} +(8.70057 + 6.32133i) q^{71} +(1.64304 - 5.05677i) q^{73} +(2.28413 - 1.65952i) q^{75} +(-0.793515 - 0.178155i) q^{77} +(-13.9778 + 10.1554i) q^{79} +(1.22295 - 3.76384i) q^{81} +(5.54039 + 4.02533i) q^{83} +(-1.92299 - 5.91836i) q^{85} -7.48318 q^{87} +13.5413 q^{89} +(-0.355336 - 1.09361i) q^{91} +(-2.21888 - 1.61211i) q^{93} +(0.755303 - 2.32458i) q^{95} +(2.74649 - 1.99544i) q^{97} +(-11.8306 - 13.4447i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{3} + q^{5} - 2 q^{7} - 8 q^{9} - 3 q^{11} - 3 q^{13} - 6 q^{15} + 7 q^{17} - 3 q^{19} + 10 q^{21} - 24 q^{23} - 16 q^{25} + q^{27} - 11 q^{29} + 14 q^{31} + q^{33} + 8 q^{35} - 17 q^{37} + 41 q^{39}+ \cdots - 28 q^{99}+O(q^{100}) $ 12 * q + q^3 + q^5 - 2 * q^7 - 8 * q^9 - 3 * q^11 - 3 * q^13 - 6 * q^15 + 7 * q^17 - 3 * q^19 + 10 * q^21 - 24 * q^23 - 16 * q^25 + q^27 - 11 * q^29 + 14 * q^31 + q^33 + 8 * q^35 - 17 * q^37 + 41 * q^39 + 10 * q^41 - 46 * q^43 + 16 * q^45 + 5 * q^47 - 5 * q^49 + 10 * q^51 - 8 * q^53 - 34 * q^55 + q^57 - 19 * q^59 + 36 * q^61 + 12 * q^63 + 28 * q^65 - 22 * q^67 - 10 * q^69 - 22 * q^71 + 12 * q^73 + 35 * q^75 + 8 * q^77 - 42 * q^79 - q^81 + 16 * q^83 + 19 * q^85 - 36 * q^87 + 26 * q^89 - 5 * q^91 + 34 * q^93 + 6 * q^95 + 34 * q^97 - 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/836\mathbb{Z}\right)^\times$.

$n$	$419$	$705$	$761$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.895600	−	2.75637i	−0.517075	−	1.59139i	−0.779475	−	0.626433i	$-0.784514\pi$
$3$	−0.895600	−	2.75637i	−0.517075	−	1.59139i	0.262401	−	0.964959i	$-0.415486\pi$
$4$		0			0
$5$	−1.97741	−	1.43667i	−0.884324	−	0.642499i	0.0500682	−	0.998746i	$-0.484056\pi$
$5$	−1.97741	−	1.43667i	−0.884324	−	0.642499i	−0.934392	+	0.356247i	$0.884056\pi$
$6$		0			0
$7$	−0.0757739	+	0.233208i	−0.0286399	+	0.0881444i	−0.964355	−	0.264613i	$-0.914756\pi$
$7$	−0.0757739	+	0.233208i	−0.0286399	+	0.0881444i	0.935715	+	0.352757i	$0.114756\pi$
$8$		0			0
$9$	−4.36844	+	3.17385i	−1.45615	+	1.05795i
$10$		0			0
$11$	0.309017	+	3.30220i	0.0931721	+	0.995650i
$11$	0.309017	+	3.30220i	0.0931721	+	0.995650i
$12$		0			0
$13$	−3.79382	+	2.75637i	−1.05222	+	0.764480i	−0.972633	−	0.232348i	$-0.925359\pi$
$13$	−3.79382	+	2.75637i	−1.05222	+	0.764480i	−0.0795838	+	0.996828i	$0.525359\pi$
$14$		0			0
$15$	−2.18903	+	6.73715i	−0.565206	+	1.73953i
$16$		0			0
$17$	2.05975	+	1.49650i	0.499562	+	0.362953i	0.808850	−	0.588015i	$-0.200091\pi$
$17$	2.05975	+	1.49650i	0.499562	+	0.362953i	−0.309287	+	0.950969i	$0.600091\pi$
$18$		0			0
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$20$		0			0
$21$	0.710671			0.155081
$22$		0			0
$23$	0.746673			0.155692			0.0778460	−	0.996965i	$-0.475196\pi$
$23$	0.746673			0.155692			0.0778460	+	0.996965i	$0.475196\pi$
$24$		0			0
$25$	0.301033	+	0.926485i	0.0602067	+	0.185297i
$26$		0			0
$27$	5.62656	+	4.08794i	1.08283	+	0.786724i
$28$		0			0
$29$	0.797879	−	2.45562i	0.148162	−	0.455997i	−0.849242	−	0.528004i	$-0.822940\pi$
$29$	0.797879	−	2.45562i	0.148162	−	0.455997i	0.997404	+	0.0720073i	$0.0229405\pi$
$30$		0			0
$31$	0.765599	−	0.556240i	0.137506	−	0.0999037i	−0.516906	−	0.856042i	$-0.672916\pi$
$31$	0.765599	−	0.556240i	0.137506	−	0.0999037i	0.654412	+	0.756138i	$0.272916\pi$
$32$		0			0
$33$	8.82533	−	3.80921i	1.53629	−	0.663099i
$34$		0			0
$35$	0.484879	−	0.352285i	0.0819596	−	0.0595471i
$36$		0			0
$37$	−0.123509	+	0.380122i	−0.0203048	+	0.0624917i	−0.960696	−	0.277604i	$-0.910460\pi$
$37$	−0.123509	+	0.380122i	−0.0203048	+	0.0624917i	0.940391	+	0.340096i	$0.110460\pi$
$38$		0			0
$39$	10.9953	+	7.98857i	1.76066	+	1.27920i
$40$		0			0
$41$	−2.62478	−	8.07825i	−0.409922	−	1.26161i	−0.916714	−	0.399543i	$-0.869169\pi$
$41$	−2.62478	−	8.07825i	−0.409922	−	1.26161i	0.506792	−	0.862068i	$-0.330831\pi$
$42$		0			0
$43$	−8.39378			−1.28004			−0.640020	−	0.768358i	$-0.721074\pi$
$43$	−8.39378			−1.28004			−0.640020	+	0.768358i	$0.721074\pi$
$44$		0			0
$45$	13.1980			1.96744
$46$		0			0
$47$	1.43142	+	4.40545i	0.208794	+	0.642601i	0.999536	+	0.0304522i	$0.00969475\pi$
$47$	1.43142	+	4.40545i	0.208794	+	0.642601i	−0.790742	+	0.612149i	$0.790305\pi$
$48$		0			0
$49$	5.61447	+	4.07915i	0.802068	+	0.582736i
$50$		0			0
$51$	2.28019	−	7.01769i	0.319290	−	0.982674i
$52$		0			0
$53$	−6.27695	+	4.56047i	−0.862206	+	0.626429i	−0.928484	−	0.371372i	$-0.878887\pi$
$53$	−6.27695	+	4.56047i	−0.862206	+	0.626429i	0.0662783	+	0.997801i	$0.478887\pi$
$54$		0			0
$55$	4.13312	−	6.97375i	0.557310	−	0.940340i
$56$		0			0
$57$	2.34471	−	1.70353i	0.310564	−	0.225638i
$58$		0			0
$59$	−3.92228	+	12.0715i	−0.510637	+	1.57158i	0.280446	+	0.959870i	$0.409518\pi$
$59$	−3.92228	+	12.0715i	−0.510637	+	1.57158i	−0.791083	+	0.611709i	$0.790482\pi$
$60$		0			0
$61$	3.33307	+	2.42162i	0.426756	+	0.310057i	0.780351	−	0.625342i	$-0.215041\pi$
$61$	3.33307	+	2.42162i	0.426756	+	0.310057i	−0.353594	+	0.935399i	$0.615041\pi$
$62$		0			0
$63$	−0.409155	−	1.25925i	−0.0515487	−	0.158651i
$64$		0			0
$65$	11.4619			1.42168
$66$		0			0
$67$	−12.4465			−1.52058			−0.760290	−	0.649584i	$-0.774943\pi$
$67$	−12.4465			−1.52058			−0.760290	+	0.649584i	$0.774943\pi$
$68$		0			0
$69$	−0.668720	−	2.05811i	−0.0805044	−	0.247767i
$70$		0			0
$71$	8.70057	+	6.32133i	1.03257	+	0.750204i	0.968821	−	0.247762i	$-0.0796950\pi$
$71$	8.70057	+	6.32133i	1.03257	+	0.750204i	0.0637468	+	0.997966i	$0.479695\pi$
$72$		0			0
$73$	1.64304	−	5.05677i	0.192304	−	0.591850i	−0.807694	−	0.589602i	$-0.799284\pi$
$73$	1.64304	−	5.05677i	0.192304	−	0.591850i	0.999997	−	0.00224784i	$-0.000715511\pi$
$74$		0			0
$75$	2.28413	−	1.65952i	0.263749	−	0.191625i
$76$		0			0
$77$	−0.793515	−	0.178155i	−0.0904294	−	0.0203027i
$78$		0			0
$79$	−13.9778	+	10.1554i	−1.57262	+	1.14258i	−0.648031	+	0.761614i	$0.724407\pi$
$79$	−13.9778	+	10.1554i	−1.57262	+	1.14258i	−0.924591	+	0.380962i	$0.875593\pi$
$80$		0			0
$81$	1.22295	−	3.76384i	0.135883	−	0.418205i
$82$		0			0
$83$	5.54039	+	4.02533i	0.608137	+	0.441837i	0.848758	−	0.528782i	$-0.177351\pi$
$83$	5.54039	+	4.02533i	0.608137	+	0.441837i	−0.240621	+	0.970619i	$0.577351\pi$
$84$		0			0
$85$	−1.92299	−	5.91836i	−0.208578	−	0.641936i
$86$		0			0
$87$	−7.48318			−0.802281
$88$		0			0
$89$	13.5413			1.43538			0.717688	−	0.696365i	$-0.245201\pi$
$89$	13.5413			1.43538			0.717688	+	0.696365i	$0.245201\pi$
$90$		0			0
$91$	−0.355336	−	1.09361i	−0.0372493	−	0.114642i
$92$		0			0
$93$	−2.21888	−	1.61211i	−0.230087	−	0.167168i
$94$		0			0
$95$	0.755303	−	2.32458i	0.0774924	−	0.238497i
$96$		0			0
$97$	2.74649	−	1.99544i	0.278864	−	0.202606i	−0.439558	−	0.898214i	$-0.644865\pi$
$97$	2.74649	−	1.99544i	0.278864	−	0.202606i	0.718422	+	0.695608i	$0.244865\pi$
$98$		0			0
$99$	−11.8306	−	13.4447i	−1.18902	−	1.35124i
$100$		0			0
$101$	1.86656	−	1.35614i	0.185730	−	0.134941i	−0.491035	−	0.871140i	$-0.663381\pi$
$101$	1.86656	−	1.35614i	0.185730	−	0.134941i	0.676765	+	0.736199i	$0.263381\pi$
$102$		0			0
$103$	−6.02034	+	18.5287i	−0.593202	+	1.82569i	−0.0297205	+	0.999558i	$0.509462\pi$
$103$	−6.02034	+	18.5287i	−0.593202	+	1.82569i	−0.563481	+	0.826129i	$0.690538\pi$
$104$		0			0
$105$	−1.40529	−	1.02100i	−0.137142	−	0.0996395i
$106$		0			0
$107$	−3.63043	−	11.1733i	−0.350967	−	1.08017i	−0.958311	−	0.285727i	$-0.907765\pi$
$107$	−3.63043	−	11.1733i	−0.350967	−	1.08017i	0.607344	−	0.794439i	$-0.292235\pi$
$108$		0			0
$109$	−8.50246			−0.814388			−0.407194	−	0.913342i	$-0.633493\pi$
$109$	−8.50246			−0.814388			−0.407194	+	0.913342i	$0.633493\pi$
$110$		0			0
$111$	1.15837			0.109948
$112$		0			0
$113$	0.706159	+	2.17333i	0.0664298	+	0.204450i	0.978762	−	0.205002i	$-0.0657200\pi$
$113$	0.706159	+	2.17333i	0.0664298	+	0.204450i	−0.912332	+	0.409452i	$0.865720\pi$
$114$		0			0
$115$	−1.47648	−	1.07272i	−0.137682	−	0.100032i
$116$		0			0
$117$	7.82474	−	24.0821i	0.723397	−	2.22639i
$118$		0			0
$119$	−0.505070	+	0.366955i	−0.0462997	+	0.0336387i
$120$		0			0
$121$	−10.8090	+	2.04087i	−0.982638	+	0.185534i
$122$		0			0
$123$	−19.9159	+	14.4698i	−1.79576	+	1.30469i
$124$		0			0
$125$	−3.04072	+	9.35839i	−0.271971	+	0.837039i
$126$		0			0
$127$	−7.17978	−	5.21641i	−0.637102	−	0.462882i	0.221751	−	0.975103i	$-0.428823\pi$
$127$	−7.17978	−	5.21641i	−0.637102	−	0.462882i	−0.858853	+	0.512221i	$0.828823\pi$
$128$		0			0
$129$	7.51747	+	23.1364i	0.661876	+	2.03705i
$130$		0			0
$131$	1.53773			0.134352			0.0671762	−	0.997741i	$-0.478601\pi$
$131$	1.53773			0.134352			0.0671762	+	0.997741i	$0.478601\pi$
$132$		0			0
$133$	−0.245210			−0.0212624
$134$		0			0
$135$	−5.25299	−	16.1670i	−0.452105	−	1.39144i
$136$		0			0
$137$	0.684374	+	0.497226i	0.0584700	+	0.0424809i	0.616636	−	0.787248i	$-0.288495\pi$
$137$	0.684374	+	0.497226i	0.0584700	+	0.0424809i	−0.558166	+	0.829729i	$0.688495\pi$
$138$		0			0
$139$	−1.58965	+	4.89243i	−0.134832	+	0.414970i	−0.995564	−	0.0940884i	$-0.970006\pi$
$139$	−1.58965	+	4.89243i	−0.134832	+	0.414970i	0.860732	+	0.509059i	$0.170006\pi$
$140$		0			0
$141$	10.8611	−	7.89104i	0.914669	−	0.664546i
$142$		0			0
$143$	−10.2744	−	11.6762i	−0.859192	−	0.976411i
$144$		0			0
$145$	−5.10565	+	3.70947i	−0.424001	+	0.308055i
$146$		0			0
$147$	6.21535	−	19.1289i	0.512633	−	1.57772i
$148$		0			0
$149$	1.57812	+	1.14657i	0.129285	+	0.0939309i	0.650548	−	0.759465i	$-0.274539\pi$
$149$	1.57812	+	1.14657i	0.129285	+	0.0939309i	−0.521264	+	0.853396i	$0.674539\pi$
$150$		0			0
$151$	−2.35175	−	7.23794i	−0.191383	−	0.589015i	−1.00000		0.000680102i	$-0.999784\pi$
$151$	−2.35175	−	7.23794i	−0.191383	−	0.589015i	0.808617	−	0.588335i	$-0.200216\pi$
$152$		0			0
$153$	−13.7475			−1.11142
$154$		0			0
$155$	−2.31304			−0.185787
$156$		0			0
$157$	−0.230082	−	0.708119i	−0.0183625	−	0.0565140i	0.941455	−	0.337138i	$-0.109459\pi$
$157$	−0.230082	−	0.708119i	−0.0183625	−	0.0565140i	−0.959818	+	0.280624i	$0.909459\pi$
$158$		0			0
$159$	18.1920	+	13.2173i	1.44272	+	1.04820i
$160$		0			0
$161$	−0.0565783	+	0.174130i	−0.00445900	+	0.0137234i
$162$		0			0
$163$	0.275083	−	0.199860i	0.0215462	−	0.0156542i	−0.576960	−	0.816772i	$-0.695761\pi$
$163$	0.275083	−	0.199860i	0.0215462	−	0.0156542i	0.598506	+	0.801118i	$0.295761\pi$
$164$		0			0
$165$	−22.9239	−	5.14673i	−1.78462	−	0.400672i
$166$		0			0
$167$	−7.87093	+	5.71857i	−0.609071	+	0.442516i	−0.849087	−	0.528253i	$-0.822847\pi$
$167$	−7.87093	+	5.71857i	−0.609071	+	0.442516i	0.240016	+	0.970769i	$0.422847\pi$
$168$		0			0
$169$	2.77827	−	8.55063i	0.213713	−	0.657740i
$170$		0			0
$171$	−4.36844	−	3.17385i	−0.334063	−	0.242711i
$172$		0			0
$173$	−4.04323	−	12.4438i	−0.307401	−	0.946084i	−0.978770	−	0.204961i	$-0.934293\pi$
$173$	−4.04323	−	12.4438i	−0.307401	−	0.946084i	0.671369	−	0.741123i	$-0.265707\pi$
$174$		0			0
$175$	−0.238874			−0.0180572
$176$		0			0
$177$	36.7864			2.76504
$178$		0			0
$179$	6.10046	+	18.7753i	0.455970	+	1.40333i	0.869993	+	0.493065i	$0.164123\pi$
$179$	6.10046	+	18.7753i	0.455970	+	1.40333i	−0.414023	+	0.910267i	$0.635877\pi$
$180$		0			0
$181$	−18.4755	−	13.4232i	−1.37327	−	0.997739i	−0.997474	−	0.0710364i	$-0.977369\pi$
$181$	−18.4755	−	13.4232i	−1.37327	−	0.997739i	−0.375796	−	0.926702i	$-0.622631\pi$
$182$		0			0
$183$	3.68978	−	11.3560i	0.272757	−	0.839459i
$184$		0			0
$185$	0.790339	−	0.574215i	0.0581069	−	0.0422171i
$186$		0			0
$187$	−4.30522	+	7.26414i	−0.314829	+	0.531206i
$188$		0			0
$189$	−1.37969	+	1.00240i	−0.100357	+	0.0729140i
$190$		0			0
$191$	−4.51907	+	13.9083i	−0.326988	+	1.00637i	0.643547	+	0.765407i	$0.277462\pi$
$191$	−4.51907	+	13.9083i	−0.326988	+	1.00637i	−0.970535	+	0.240960i	$0.922538\pi$
$192$		0			0
$193$	−15.9427	−	11.5831i	−1.14758	−	0.833768i	−0.159425	−	0.987210i	$-0.550964\pi$
$193$	−15.9427	−	11.5831i	−1.14758	−	0.833768i	−0.988158	+	0.153442i	$0.950964\pi$
$194$		0			0
$195$	−10.2653	−	31.5933i	−0.735113	−	2.26245i
$196$		0			0
$197$	−10.2015			−0.726828			−0.363414	−	0.931628i	$-0.618389\pi$
$197$	−10.2015			−0.726828			−0.363414	+	0.931628i	$0.618389\pi$
$198$		0			0
$199$	−2.22847			−0.157972			−0.0789860	−	0.996876i	$-0.525168\pi$
$199$	−2.22847			−0.157972			−0.0789860	+	0.996876i	$0.525168\pi$
$200$		0			0
$201$	11.1471	+	34.3071i	0.786253	+	2.41984i
$202$		0			0
$203$	0.512212	+	0.372144i	0.0359502	+	0.0261194i
$204$		0			0
$205$	−6.41552	+	19.7450i	−0.448080	+	1.37905i
$206$		0			0
$207$	−3.26179	+	2.36983i	−0.226710	+	0.164715i
$208$		0			0
$209$	−3.04508	+	1.31433i	−0.210633	+	0.0909140i
$210$		0			0
$211$	12.0746	−	8.77271i	0.831250	−	0.603938i	−0.0886630	−	0.996062i	$-0.528259\pi$
$211$	12.0746	−	8.77271i	0.831250	−	0.603938i	0.919913	+	0.392124i	$0.128259\pi$
$212$		0			0
$213$	9.63172	−	29.6434i	0.659955	−	2.03113i
$214$		0			0
$215$	16.5979	+	12.0591i	1.13197	+	0.822424i
$216$		0			0
$217$	0.0717073	+	0.220692i	0.00486781	+	0.0149816i
$218$		0			0
$219$	−15.4098			−1.04130
$220$		0			0
$221$	−11.9392			−0.803118
$222$		0			0
$223$	−4.96289	−	15.2742i	−0.332339	−	1.02284i	−0.968018	−	0.250882i	$-0.919280\pi$
$223$	−4.96289	−	15.2742i	−0.332339	−	1.02284i	0.635678	−	0.771954i	$-0.280720\pi$
$224$		0			0
$225$	−4.25557	−	3.09186i	−0.283705	−	0.206124i
$226$		0			0
$227$	4.94001	−	15.2038i	0.327880	−	1.00911i	−0.642244	−	0.766501i	$-0.721996\pi$
$227$	4.94001	−	15.2038i	0.327880	−	1.00911i	0.970124	−	0.242611i	$-0.0780038\pi$
$228$		0			0
$229$	−15.3683	+	11.1657i	−1.01557	+	0.737853i	−0.965370	−	0.260886i	$-0.915985\pi$
$229$	−15.3683	+	11.1657i	−1.01557	+	0.737853i	−0.0501984	+	0.998739i	$0.515985\pi$
$230$		0			0
$231$	0.219610	+	2.34678i	0.0144492	+	0.154407i
$232$		0			0
$233$	10.2247	−	7.42867i	0.669842	−	0.486669i	−0.200130	−	0.979769i	$-0.564137\pi$
$233$	10.2247	−	7.42867i	0.669842	−	0.486669i	0.869972	+	0.493101i	$0.164137\pi$
$234$		0			0
$235$	3.49869	−	10.7679i	0.228229	−	0.702417i
$236$		0			0
$237$	40.5107	+	29.4327i	2.63145	+	1.91186i
$238$		0			0
$239$	6.10415	+	18.7866i	0.394845	+	1.21521i	0.929082	+	0.369873i	$0.120599\pi$
$239$	6.10415	+	18.7866i	0.394845	+	1.21521i	−0.534238	+	0.845334i	$0.679401\pi$
$240$		0			0
$241$	9.93140			0.639738			0.319869	−	0.947462i	$-0.396361\pi$
$241$	9.93140			0.639738			0.319869	+	0.947462i	$0.396361\pi$
$242$		0			0
$243$	9.39463			0.602666
$244$		0			0
$245$	−5.24170	−	16.1323i	−0.334880	−	1.03066i
$246$		0			0
$247$	−3.79382	−	2.75637i	−0.241395	−	0.175384i
$248$		0			0
$249$	6.13333	−	18.8765i	0.388684	−	1.19625i
$250$		0			0
$251$	16.9914	−	12.3449i	1.07249	−	0.779206i	0.0961281	−	0.995369i	$-0.469354\pi$
$251$	16.9914	−	12.3449i	1.07249	−	0.779206i	0.976357	+	0.216163i	$0.0693542\pi$
$252$		0			0
$253$	0.230735	+	2.46566i	0.0145062	+	0.155015i
$254$		0			0
$255$	−14.5910	+	10.6010i	−0.913722	+	0.663858i
$256$		0			0
$257$	3.61211	−	11.1169i	0.225317	−	0.693455i	−0.772942	−	0.634476i	$-0.781216\pi$
$257$	3.61211	−	11.1169i	0.225317	−	0.693455i	0.998259	−	0.0589783i	$-0.0187843\pi$
$258$		0			0
$259$	−0.0792889	−	0.0576067i	−0.00492677	−	0.00357951i
$260$		0			0
$261$	4.30830	+	13.2596i	0.266677	+	0.820747i
$262$		0			0
$263$	−22.2357			−1.37111			−0.685556	−	0.728020i	$-0.740441\pi$
$263$	−22.2357			−1.37111			−0.685556	+	0.728020i	$0.740441\pi$
$264$		0			0
$265$	18.9640			1.16495
$266$		0			0
$267$	−12.1276	−	37.3249i	−0.742196	−	2.28425i
$268$		0			0
$269$	2.00220	+	1.45469i	0.122076	+	0.0886937i	0.647148	−	0.762364i	$-0.275962\pi$
$269$	2.00220	+	1.45469i	0.122076	+	0.0886937i	−0.525072	+	0.851058i	$0.675962\pi$
$270$		0			0
$271$	5.09451	−	15.6793i	0.309469	−	0.952448i	−0.668502	−	0.743710i	$-0.733064\pi$
$271$	5.09451	−	15.6793i	0.309469	−	0.952448i	0.977972	−	0.208738i	$-0.0669357\pi$
$272$		0			0
$273$	−2.69616	+	1.95887i	−0.163179	+	0.118557i
$274$		0			0
$275$	−2.96641	+	1.28037i	−0.178881	+	0.0772093i
$276$		0			0
$277$	−9.03711	+	6.56585i	−0.542988	+	0.394504i	−0.825193	−	0.564850i	$-0.808934\pi$
$277$	−9.03711	+	6.56585i	−0.542988	+	0.394504i	0.282206	+	0.959354i	$0.408934\pi$
$278$		0			0
$279$	−1.57904	+	4.85980i	−0.0945349	+	0.290949i
$280$		0			0
$281$	−4.71551	−	3.42602i	−0.281304	−	0.204379i	0.438182	−	0.898886i	$-0.355623\pi$
$281$	−4.71551	−	3.42602i	−0.281304	−	0.204379i	−0.719486	+	0.694507i	$0.755623\pi$
$282$		0			0
$283$	0.193750	+	0.596301i	0.0115172	+	0.0354464i	0.956650	−	0.291240i	$-0.0940679\pi$
$283$	0.193750	+	0.596301i	0.0115172	+	0.0354464i	−0.945133	+	0.326687i	$0.894068\pi$
$284$		0			0
$285$	−7.08386			−0.419612
$286$		0			0
$287$	2.08280			0.122944
$288$		0			0
$289$	−3.25022	−	10.0032i	−0.191189	−	0.588421i
$290$		0			0
$291$	−7.95994	−	5.78323i	−0.466620	−	0.339019i
$292$		0			0
$293$	3.01168	−	9.26898i	0.175944	−	0.541500i	−0.823731	−	0.566980i	$-0.808112\pi$
$293$	3.01168	−	9.26898i	0.175944	−	0.541500i	0.999675	+	0.0254805i	$0.00811157\pi$
$294$		0			0
$295$	25.0987	−	18.2353i	1.46131	−	1.06170i
$296$		0			0
$297$	−11.7605	+	19.8433i	−0.682412	+	1.15142i
$298$		0			0
$299$	−2.83274	+	2.05811i	−0.163822	+	0.119023i
$300$		0			0
$301$	0.636030	−	1.95750i	0.0366602	−	0.112828i
$302$		0			0
$303$	−5.40971	−	3.93039i	−0.310780	−	0.225795i
$304$		0			0
$305$	−3.11177	−	9.57706i	−0.178180	−	0.548381i
$306$		0			0
$307$	24.9571			1.42437			0.712187	−	0.701989i	$-0.247705\pi$
$307$	24.9571			1.42437			0.712187	+	0.701989i	$0.247705\pi$
$308$		0			0
$309$	56.4638			3.21211
$310$		0			0
$311$	−3.21137	−	9.88359i	−0.182100	−	0.560447i	0.817786	−	0.575522i	$-0.195201\pi$
$311$	−3.21137	−	9.88359i	−0.182100	−	0.560447i	−0.999886	+	0.0150752i	$0.995201\pi$
$312$		0			0
$313$	20.3986	+	14.8204i	1.15300	+	0.837700i	0.988876	−	0.148740i	$-0.0475219\pi$
$313$	20.3986	+	14.8204i	1.15300	+	0.837700i	0.164119	+	0.986441i	$0.447522\pi$
$314$		0			0
$315$	−1.00006	+	3.07787i	−0.0563471	+	0.173418i
$316$		0			0
$317$	−8.77163	+	6.37296i	−0.492664	+	0.357941i	−0.806208	−	0.591633i	$-0.798484\pi$
$317$	−8.77163	+	6.37296i	−0.492664	+	0.357941i	0.313544	+	0.949574i	$0.398484\pi$
$318$		0			0
$319$	8.35550	+	1.87593i	0.467818	+	0.105032i
$320$		0			0
$321$	−27.5464	+	20.0137i	−1.53749	+	1.11705i
$322$		0			0
$323$	−0.786754	+	2.42138i	−0.0437762	+	0.134729i
$324$		0			0
$325$	−3.69580	−	2.68516i	−0.205006	−	0.148946i
$326$		0			0
$327$	7.61480	+	23.4359i	0.421099	+	1.29601i
$328$		0			0
$329$	−1.13585			−0.0626215
$330$		0			0
$331$	−24.6664			−1.35579			−0.677893	−	0.735160i	$-0.737107\pi$
$331$	−24.6664			−1.35579			−0.677893	+	0.735160i	$0.737107\pi$
$332$		0			0
$333$	−0.666911	−	2.05254i	−0.0365465	−	0.112479i
$334$		0			0
$335$	24.6118	+	17.8815i	1.34468	+	0.976970i
$336$		0			0
$337$	−3.01515	+	9.27969i	−0.164246	+	0.505497i	−0.998980	−	0.0451565i	$-0.985621\pi$
$337$	−3.01515	+	9.27969i	−0.164246	+	0.505497i	0.834734	+	0.550653i	$0.185621\pi$
$338$		0			0
$339$	5.35808	−	3.89287i	0.291011	−	0.211432i
$340$		0			0
$341$	2.07340	+	2.35627i	0.112281	+	0.127599i
$342$		0			0
$343$	−2.76537	+	2.00916i	−0.149316	+	0.108485i
$344$		0			0
$345$	−1.63449	+	5.03045i	−0.0879981	+	0.270830i
$346$		0			0
$347$	−9.18666	−	6.67450i	−0.493166	−	0.358306i	0.313235	−	0.949676i	$-0.398587\pi$
$347$	−9.18666	−	6.67450i	−0.493166	−	0.358306i	−0.806401	+	0.591370i	$0.798587\pi$
$348$		0			0
$349$	6.10663	+	18.7943i	0.326880	+	1.00603i	0.970585	+	0.240760i	$0.0773967\pi$
$349$	6.10663	+	18.7943i	0.326880	+	1.00603i	−0.643704	+	0.765274i	$0.722603\pi$
$350$		0			0
$351$	−32.6141			−1.74081
$352$		0			0
$353$	17.4515			0.928850			0.464425	−	0.885612i	$-0.346261\pi$
$353$	17.4515			0.928850			0.464425	+	0.885612i	$0.346261\pi$
$354$		0			0
$355$	−8.12290	−	24.9997i	−0.431119	−	1.32685i
$356$		0			0
$357$	1.46380	+	1.06352i	0.0774728	+	0.0562873i
$358$		0			0
$359$	−9.23780	+	28.4310i	−0.487553	+	1.50053i	0.340697	+	0.940173i	$0.389337\pi$
$359$	−9.23780	+	28.4310i	−0.487553	+	1.50053i	−0.828249	+	0.560360i	$0.810663\pi$
$360$		0			0
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$		0			0
$363$	15.3059	+	27.9659i	0.803354	+	1.46783i
$364$		0			0
$365$	−10.5139	+	7.63878i	−0.550322	+	0.399832i
$366$		0			0
$367$	−5.23188	+	16.1021i	−0.273102	+	0.840522i	0.716613	+	0.697471i	$0.245691\pi$
$367$	−5.23188	+	16.1021i	−0.273102	+	0.840522i	−0.989715	+	0.143051i	$0.954309\pi$
$368$		0			0
$369$	37.1054	+	26.9587i	1.93163	+	1.40341i
$370$		0			0
$371$	−0.587910	−	1.80940i	−0.0305228	−	0.0939395i
$372$		0			0
$373$	−24.4999			−1.26856			−0.634278	−	0.773105i	$-0.718703\pi$
$373$	−24.4999			−1.26856			−0.634278	+	0.773105i	$0.718703\pi$
$374$		0			0
$375$	28.5185			1.47269
$376$		0			0
$377$	3.74159	+	11.5154i	0.192702	+	0.593075i
$378$		0			0
$379$	−10.9784	−	7.97631i	−0.563925	−	0.409716i	0.268968	−	0.963149i	$-0.413317\pi$
$379$	−10.9784	−	7.97631i	−0.563925	−	0.409716i	−0.832893	+	0.553434i	$0.813317\pi$
$380$		0			0
$381$	−7.94817	+	24.4620i	−0.407197	+	1.25322i
$382$		0			0
$383$	−28.3474	+	20.5956i	−1.44848	+	1.05238i	−0.462300	+	0.886724i	$0.652976\pi$
$383$	−28.3474	+	20.5956i	−1.44848	+	1.05238i	−0.986183	+	0.165660i	$0.947024\pi$
$384$		0			0
$385$	1.31315	+	1.49231i	0.0669244	+	0.0760549i
$386$		0			0
$387$	36.6677	−	26.6406i	1.86392	−	1.35422i
$388$		0			0
$389$	0.718994	−	2.21284i	0.0364544	−	0.112195i	−0.931173	−	0.364577i	$-0.881214\pi$
$389$	0.718994	−	2.21284i	0.0364544	−	0.112195i	0.967628	+	0.252381i	$0.0812137\pi$
$390$		0			0
$391$	1.53796	+	1.11739i	0.0777779	+	0.0565090i
$392$		0			0
$393$	−1.37719	−	4.23856i	−0.0694702	−	0.213807i
$394$		0			0
$395$	42.2298			2.12481
$396$		0			0
$397$	−6.30592			−0.316485			−0.158243	−	0.987400i	$-0.550583\pi$
$397$	−6.30592			−0.316485			−0.158243	+	0.987400i	$0.550583\pi$
$398$		0			0
$399$	0.219610	+	0.675889i	0.0109942	+	0.0338368i
$400$		0			0
$401$	17.0454	+	12.3842i	0.851209	+	0.618439i	0.925479	−	0.378799i	$-0.123663\pi$
$401$	17.0454	+	12.3842i	0.851209	+	0.618439i	−0.0742704	+	0.997238i	$0.523663\pi$
$402$		0			0
$403$	−1.37134	+	4.22055i	−0.0683113	+	0.210241i
$404$		0			0
$405$	−7.82567	+	5.68568i	−0.388861	+	0.282524i
$406$		0			0
$407$	−1.29341	−	0.290388i	−0.0641117	−	0.0143940i
$408$		0			0
$409$	−11.9582	+	8.68813i	−0.591294	+	0.429601i	−0.842778	−	0.538261i	$-0.819081\pi$
$409$	−11.9582	+	8.68813i	−0.591294	+	0.429601i	0.251484	+	0.967862i	$0.419081\pi$
$410$		0			0
$411$	0.757616	−	2.33170i	0.0373705	−	0.115014i
$412$		0			0
$413$	−2.51797	−	1.82941i	−0.123901	−	0.0900196i
$414$		0			0
$415$	−5.17254	−	15.9194i	−0.253910	−	0.781454i
$416$		0			0
$417$	14.9090			0.730099
$418$		0			0
$419$	−27.3428			−1.33578			−0.667891	−	0.744259i	$-0.732803\pi$
$419$	−27.3428			−1.33578			−0.667891	+	0.744259i	$0.732803\pi$
$420$		0			0
$421$	−9.17036	−	28.2235i	−0.446936	−	1.37553i	−0.880347	−	0.474331i	$-0.842690\pi$
$421$	−9.17036	−	28.2235i	−0.446936	−	1.37553i	0.433411	−	0.901197i	$-0.357310\pi$
$422$		0			0
$423$	−20.2353	−	14.7018i	−0.983875	−	0.714827i
$424$		0			0
$425$	−0.766428	+	2.35882i	−0.0371772	+	0.114420i
$426$		0			0
$427$	−0.817301	+	0.593804i	−0.0395520	+	0.0287362i
$428$		0			0
$429$	−22.9821	+	38.7774i	−1.10959	+	1.87219i
$430$		0			0
$431$	−8.46886	+	6.15298i	−0.407930	+	0.296379i	−0.772763	−	0.634694i	$-0.781126\pi$
$431$	−8.46886	+	6.15298i	−0.407930	+	0.296379i	0.364833	+	0.931073i	$0.381126\pi$
$432$		0			0
$433$	−1.80562	+	5.55714i	−0.0867728	+	0.267059i	−0.985022	−	0.172426i	$-0.944839\pi$
$433$	−1.80562	+	5.55714i	−0.0867728	+	0.267059i	0.898250	+	0.439486i	$0.144839\pi$
$434$		0			0
$435$	14.7973	+	10.7509i	0.709476	+	0.515465i
$436$		0			0
$437$	0.230735	+	0.710128i	0.0110375	+	0.0339700i
$438$		0			0
$439$	34.1518			1.62998			0.814988	−	0.579478i	$-0.196743\pi$
$439$	34.1518			1.62998			0.814988	+	0.579478i	$0.196743\pi$
$440$		0			0
$441$	−37.4731			−1.78443
$442$		0			0
$443$	5.74940	+	17.6948i	0.273162	+	0.840707i	0.989700	+	0.143158i	$0.0457258\pi$
$443$	5.74940	+	17.6948i	0.273162	+	0.840707i	−0.716538	+	0.697548i	$0.754274\pi$
$444$		0			0
$445$	−26.7767	−	19.4544i	−1.26934	−	0.922227i
$446$		0			0
$447$	1.74701	−	5.37676i	0.0826310	−	0.254312i
$448$		0			0
$449$	26.8588	−	19.5141i	1.26755	−	0.920925i	0.268443	−	0.963296i	$-0.413491\pi$
$449$	26.8588	−	19.5141i	1.26755	−	0.920925i	0.999102	+	0.0423701i	$0.0134909\pi$
$450$		0			0
$451$	25.8649	−	11.1639i	1.21793	−	0.525686i
$452$		0			0
$453$	−17.8442	+	12.9646i	−0.838395	+	0.609130i
$454$		0			0
$455$	−0.868515	+	2.67302i	−0.0407166	+	0.125313i
$456$		0			0
$457$	−30.2670	−	21.9902i	−1.41583	−	1.02866i	−0.992442	−	0.122711i	$-0.960841\pi$
$457$	−30.2670	−	21.9902i	−1.41583	−	1.02866i	−0.423387	−	0.905949i	$-0.639159\pi$
$458$		0			0
$459$	5.47173	+	16.8403i	0.255398	+	0.786036i
$460$		0			0
$461$	−26.7838			−1.24744			−0.623722	−	0.781646i	$-0.714380\pi$
$461$	−26.7838			−1.24744			−0.623722	+	0.781646i	$0.714380\pi$
$462$		0			0
$463$	−18.0638			−0.839494			−0.419747	−	0.907641i	$-0.637881\pi$
$463$	−18.0638			−0.839494			−0.419747	+	0.907641i	$0.637881\pi$
$464$		0			0
$465$	2.07155	+	6.37559i	0.0960660	+	0.295661i
$466$		0			0
$467$	−0.577782	−	0.419783i	−0.0267366	−	0.0194252i	0.574337	−	0.818619i	$-0.305260\pi$
$467$	−0.577782	−	0.419783i	−0.0267366	−	0.0194252i	−0.601073	+	0.799194i	$0.705260\pi$
$468$		0			0
$469$	0.943119	−	2.90262i	0.0435492	−	0.134031i
$470$		0			0
$471$	−1.74578	+	1.26838i	−0.0804412	+	0.0584439i
$472$		0			0
$473$	−2.59382	−	27.7179i	−0.119264	−	1.27447i
$474$		0			0
$475$	−0.788115	+	0.572599i	−0.0361612	+	0.0262727i
$476$		0			0
$477$	12.9462	−	39.8443i	0.592765	−	1.82434i
$478$		0			0
$479$	26.0992	+	18.9622i	1.19250	+	0.866405i	0.993527	−	0.113599i	$-0.0362380\pi$
$479$	26.0992	+	18.9622i	1.19250	+	0.866405i	0.198977	+	0.980004i	$0.436238\pi$
$480$		0			0
$481$	−0.579187	−	1.78255i	−0.0264086	−	0.0812775i
$482$		0			0
$483$	0.530639			0.0241449
$484$		0			0
$485$	−8.29772			−0.376780
$486$		0			0
$487$	1.43658	+	4.42133i	0.0650975	+	0.200349i	0.978315	−	0.207123i	$-0.0664101\pi$
$487$	1.43658	+	4.42133i	0.0650975	+	0.200349i	−0.913217	+	0.407473i	$0.866410\pi$
$488$		0			0
$489$	−0.797252	−	0.579238i	−0.0360530	−	0.0261940i
$490$		0			0
$491$	−10.4347	+	32.1148i	−0.470912	+	1.44932i	0.380480	+	0.924789i	$0.375759\pi$
$491$	−10.4347	+	32.1148i	−0.470912	+	1.44932i	−0.851392	+	0.524530i	$0.824241\pi$
$492$		0			0
$493$	5.31825	−	3.86394i	0.239522	−	0.174023i
$494$		0			0
$495$	4.07840	+	43.5823i	0.183310	+	1.95888i
$496$		0			0
$497$	−2.13346	+	1.55005i	−0.0956989	+	0.0695293i
$498$		0			0
$499$	−8.40010	+	25.8529i	−0.376040	+	1.15733i	0.566734	+	0.823901i	$0.308207\pi$
$499$	−8.40010	+	25.8529i	−0.376040	+	1.15733i	−0.942774	+	0.333432i	$0.891793\pi$
$500$		0			0
$501$	22.8117	+	16.5737i	1.01915	+	0.740457i
$502$		0			0
$503$	−13.0527	−	40.1721i	−0.581991	−	1.79118i	−0.611031	−	0.791606i	$-0.709245\pi$
$503$	−13.0527	−	40.1721i	−0.581991	−	1.79118i	0.0290401	−	0.999578i	$-0.490755\pi$
$504$		0			0
$505$	−5.63928			−0.250945
$506$		0			0
$507$	−26.0569			−1.15723
$508$		0			0
$509$	−9.05662	−	27.8734i	−0.401428	−	1.23547i	−0.923842	−	0.382775i	$-0.874968\pi$
$509$	−9.05662	−	27.8734i	−0.401428	−	1.23547i	0.522414	−	0.852692i	$-0.325032\pi$
$510$		0			0
$511$	1.05478	+	0.766343i	0.0466607	+	0.0339010i
$512$		0			0
$513$	−2.14916	+	6.61442i	−0.0948876	+	0.292034i
$514$		0			0
$515$	38.5243	−	27.9895i	1.69758	−	1.23337i
$516$		0			0
$517$	−14.1053	+	6.08819i	−0.620352	+	0.267758i
$518$		0			0
$519$	−30.6786	+	22.2893i	−1.34664	+	0.978392i
$520$		0			0
$521$	1.06580	−	3.28019i	0.0466935	−	0.143708i	−0.924992	−	0.379988i	$-0.875928\pi$
$521$	1.06580	−	3.28019i	0.0466935	−	0.143708i	0.971685	+	0.236280i	$0.0759282\pi$
$522$		0			0
$523$	21.2348	+	15.4280i	0.928534	+	0.674619i	0.945633	−	0.325234i	$-0.105443\pi$
$523$	21.2348	+	15.4280i	0.928534	+	0.674619i	−0.0170996	+	0.999854i	$0.505443\pi$
$524$		0			0
$525$	0.213936	+	0.658427i	0.00933692	+	0.0287361i
$526$		0			0
$527$	2.40935			0.104953
$528$		0			0
$529$	−22.4425			−0.975760
$530$		0			0
$531$	−21.1791	−	65.1824i	−0.919093	−	2.82868i
$532$		0			0
$533$	32.2246	+	23.4126i	1.39580	+	1.01411i
$534$		0			0
$535$	−8.87354	+	27.3100i	−0.383637	+	1.18071i
$536$		0			0
$537$	46.2881	−	33.6303i	1.99748	−	1.45125i
$538$		0			0
$539$	−11.7352	+	19.8006i	−0.505471	+	0.852874i
$540$		0			0
$541$	22.4023	−	16.2762i	0.963149	−	0.699768i	0.00926880	−	0.999957i	$-0.497050\pi$
$541$	22.4023	−	16.2762i	0.963149	−	0.699768i	0.953880	+	0.300189i	$0.0970496\pi$
$542$		0			0
$543$	−20.4527	+	62.9470i	−0.877711	+	2.70132i
$544$		0			0
$545$	16.8128	+	12.2152i	0.720183	+	0.523243i
$546$		0			0
$547$	9.79361	+	30.1416i	0.418745	+	1.28876i	0.908858	+	0.417105i	$0.136955\pi$
$547$	9.79361	+	30.1416i	0.418745	+	1.28876i	−0.490114	+	0.871658i	$0.663045\pi$
$548$		0			0
$549$	−22.2462			−0.949444
$550$		0			0
$551$	2.58199			0.109997
$552$		0			0
$553$	−1.30918	−	4.02925i	−0.0556721	−	0.171341i
$554$		0			0
$555$	−2.29058	−	1.66420i	−0.0972296	−	0.0706414i
$556$		0			0
$557$	9.65360	−	29.7107i	0.409036	−	1.25888i	−0.508441	−	0.861097i	$-0.669778\pi$
$557$	9.65360	−	29.7107i	0.409036	−	1.25888i	0.917478	−	0.397788i	$-0.130222\pi$
$558$		0			0
$559$	31.8445	−	23.1364i	1.34688	−	0.978565i
$560$		0			0
$561$	23.8784	+	5.36104i	1.00815	+	0.226343i
$562$		0			0
$563$	31.5220	−	22.9021i	1.32850	−	0.965209i	0.328712	−	0.944430i	$-0.393385\pi$
$563$	31.5220	−	22.9021i	1.32850	−	0.965209i	0.999784	−	0.0207786i	$-0.00661451\pi$
$564$		0			0
$565$	1.72600	−	5.31208i	0.0726134	−	0.223481i
$566$		0			0
$567$	0.785091	+	0.570402i	0.0329707	+	0.0239546i
$568$		0			0
$569$	−3.66189	−	11.2701i	−0.153514	−	0.472469i	0.844493	−	0.535567i	$-0.179902\pi$
$569$	−3.66189	−	11.2701i	−0.153514	−	0.472469i	−0.998007	+	0.0630978i	$0.979902\pi$
$570$		0			0
$571$	37.4316			1.56646			0.783231	−	0.621731i	$-0.213570\pi$
$571$	37.4316			1.56646			0.783231	+	0.621731i	$0.213570\pi$
$572$		0			0
$573$	42.3836			1.77060
$574$		0			0
$575$	0.224773	+	0.691782i	0.00937370	+	0.0288493i
$576$		0			0
$577$	3.18749	+	2.31585i	0.132697	+	0.0964100i	0.652154	−	0.758087i	$-0.273866\pi$
$577$	3.18749	+	2.31585i	0.132697	+	0.0964100i	−0.519457	+	0.854497i	$0.673866\pi$
$578$		0			0
$579$	−17.6490	+	54.3179i	−0.733465	+	2.25737i
$580$		0			0
$581$	−1.35856	+	0.987049i	−0.0563624	+	0.0409497i
$582$		0			0
$583$	−16.9993	−	19.3185i	−0.704038	−	0.800090i
$584$		0			0
$585$	−50.0707	+	36.3785i	−2.07017	+	1.50407i
$586$		0			0
$587$	−0.187232	+	0.576240i	−0.00772788	+	0.0237840i	−0.954846	−	0.297101i	$-0.903980\pi$
$587$	−0.187232	+	0.576240i	−0.00772788	+	0.0237840i	0.947118	+	0.320885i	$0.103980\pi$
$588$		0			0
$589$	0.765599	+	0.556240i	0.0315460	+	0.0229195i
$590$		0			0
$591$	9.13648	+	28.1192i	0.375824	+	1.15667i
$592$		0			0
$593$	35.8849			1.47362			0.736809	−	0.676101i	$-0.236332\pi$
$593$	35.8849			1.47362			0.736809	+	0.676101i	$0.236332\pi$
$594$		0			0
$595$	1.52592			0.0625567
$596$		0			0
$597$	1.99582	+	6.14249i	0.0816833	+	0.251395i
$598$		0			0
$599$	3.59807	+	2.61415i	0.147013	+	0.106811i	0.658861	−	0.752265i	$-0.271039\pi$
$599$	3.59807	+	2.61415i	0.147013	+	0.106811i	−0.511847	+	0.859076i	$0.671039\pi$
$600$		0			0
$601$	−9.55433	+	29.4052i	−0.389729	+	1.19946i	0.543262	+	0.839563i	$0.317189\pi$
$601$	−9.55433	+	29.4052i	−0.389729	+	1.19946i	−0.932991	+	0.359900i	$0.882811\pi$
$602$		0			0
$603$	54.3717	−	39.5033i	2.21418	−	1.60870i
$604$		0			0
$605$	24.3059	+	11.4934i	0.988175	+	0.467272i
$606$		0			0
$607$	24.8567	−	18.0594i	1.00890	−	0.733010i	0.0449229	−	0.998990i	$-0.485696\pi$
$607$	24.8567	−	18.0594i	1.00890	−	0.733010i	0.963978	+	0.265981i	$0.0856958\pi$
$608$		0			0
$609$	0.567030	−	1.74514i	0.0229772	−	0.0707166i
$610$		0			0
$611$	−17.5736	−	12.7680i	−0.710952	−	0.516537i
$612$		0			0
$613$	−5.90798	−	18.1829i	−0.238621	−	0.734400i	−0.996620	−	0.0821449i	$-0.973823\pi$
$613$	−5.90798	−	18.1829i	−0.238621	−	0.734400i	0.757999	−	0.652255i	$-0.226177\pi$
$614$		0			0
$615$	60.1702			2.42630
$616$		0			0
$617$	−24.1217			−0.971102			−0.485551	−	0.874208i	$-0.661381\pi$
$617$	−24.1217			−0.971102			−0.485551	+	0.874208i	$0.661381\pi$
$618$		0			0
$619$	−10.7776	−	33.1700i	−0.433187	−	1.33321i	−0.894933	−	0.446201i	$-0.852777\pi$
$619$	−10.7776	−	33.1700i	−0.433187	−	1.33321i	0.461745	−	0.887013i	$-0.347223\pi$
$620$		0			0
$621$	4.20120	+	3.05235i	0.168588	+	0.122487i
$622$		0			0
$623$	−1.02608	+	3.15794i	−0.0411089	+	0.126520i
$624$		0			0
$625$	23.3982	−	16.9998i	0.935930	−	0.679993i
$626$		0			0
$627$	6.34995	+	7.21628i	0.253593	+	0.288190i
$628$		0			0
$629$	−0.823249	+	0.598126i	−0.0328251	+	0.0238488i
$630$		0			0
$631$	9.49259	−	29.2152i	0.377894	−	1.16304i	−0.563611	−	0.826040i	$-0.690588\pi$
$631$	9.49259	−	29.2152i	0.377894	−	1.16304i	0.941505	−	0.336998i	$-0.109412\pi$
$632$		0			0
$633$	−34.9948	−	25.4252i	−1.39092	−	1.01056i
$634$		0			0
$635$	6.70308	+	20.6300i	0.266004	+	0.818675i
$636$		0			0
$637$	−32.5440			−1.28944
$638$		0			0
$639$	−58.0709			−2.29725
$640$		0			0
$641$	−12.5569	−	38.6460i	−0.495966	−	1.52643i	−0.815446	−	0.578834i	$-0.803508\pi$
$641$	−12.5569	−	38.6460i	−0.495966	−	1.52643i	0.319480	−	0.947593i	$-0.396492\pi$
$642$		0			0
$643$	−9.71973	−	7.06180i	−0.383309	−	0.278490i	0.379399	−	0.925233i	$-0.376131\pi$
$643$	−9.71973	−	7.06180i	−0.383309	−	0.278490i	−0.762708	+	0.646743i	$0.776131\pi$
$644$		0			0
$645$	18.3743	−	56.5502i	0.723486	−	2.22666i
$646$		0			0
$647$	3.86706	−	2.80958i	0.152030	−	0.110456i	−0.509170	−	0.860666i	$-0.670048\pi$
$647$	3.86706	−	2.80958i	0.152030	−	0.110456i	0.661200	+	0.750210i	$0.270048\pi$
$648$		0			0
$649$	−41.0746	−	9.22183i	−1.61232	−	0.361988i
$650$		0			0
$651$	0.544089	−	0.395304i	0.0213245	−	0.0154932i
$652$		0			0
$653$	5.14169	−	15.8245i	0.201210	−	0.619260i	−0.798638	−	0.601812i	$-0.794446\pi$
$653$	5.14169	−	15.8245i	0.201210	−	0.619260i	0.999848	−	0.0174482i	$-0.00555422\pi$
$654$		0			0
$655$	−3.04072	−	2.20922i	−0.118811	−	0.0863212i
$656$		0			0
$657$	8.87192	+	27.3050i	0.346127	+	1.06527i
$658$		0			0
$659$	44.4696			1.73229			0.866145	−	0.499792i	$-0.166590\pi$
$659$	44.4696			1.73229			0.866145	+	0.499792i	$0.166590\pi$
$660$		0			0
$661$	−6.28473			−0.244448			−0.122224	−	0.992503i	$-0.539003\pi$
$661$	−6.28473			−0.244448			−0.122224	+	0.992503i	$0.539003\pi$
$662$		0			0
$663$	10.6928	+	32.9089i	0.415272	+	1.27808i
$664$		0			0
$665$	0.484879	+	0.352285i	0.0188028	+	0.0136610i
$666$		0			0
$667$	0.595755	−	1.83354i	0.0230677	−	0.0709951i
$668$		0			0
$669$	−37.6566	+	27.3591i	−1.45589	+	1.05776i
$670$		0			0
$671$	−6.96669	+	11.7548i	−0.268946	+	0.453788i
$672$		0			0
$673$	3.88033	−	2.81922i	0.149576	−	0.108673i	−0.510481	−	0.859889i	$-0.670532\pi$
$673$	3.88033	−	2.81922i	0.149576	−	0.108673i	0.660056	+	0.751216i	$0.270532\pi$
$674$		0			0
$675$	−2.09363	+	6.44353i	−0.0805839	+	0.248012i
$676$		0			0
$677$	18.9326	+	13.7553i	0.727638	+	0.528660i	0.888815	−	0.458265i	$-0.151529\pi$
$677$	18.9326	+	13.7553i	0.727638	+	0.528660i	−0.161177	+	0.986925i	$0.551529\pi$
$678$		0			0
$679$	0.257241	+	0.791706i	0.00987200	+	0.0303829i
$680$		0			0
$681$	−46.3316			−1.77543
$682$		0			0
$683$	17.8739			0.683926			0.341963	−	0.939713i	$-0.388908\pi$
$683$	17.8739			0.683926			0.341963	+	0.939713i	$0.388908\pi$
$684$		0			0
$685$	−0.638935	−	1.96644i	−0.0244124	−	0.0751338i
$686$		0			0
$687$	44.5408	+	32.3608i	1.69934	+	1.23464i
$688$		0			0
$689$	11.2433	−	34.6032i	0.428335	−	1.31828i
$690$		0			0
$691$	−3.40057	+	2.47066i	−0.129364	+	0.0939883i	−0.650586	−	0.759433i	$-0.725476\pi$
$691$	−3.40057	+	2.47066i	−0.129364	+	0.0939883i	0.521222	+	0.853421i	$0.325476\pi$
$692$		0			0
$693$	4.03186	−	1.74024i	0.153158	−	0.0661063i
$694$		0			0
$695$	10.1722	−	7.39053i	0.385853	−	0.280339i
$696$		0			0
$697$	6.68267	−	20.5671i	0.253124	−	0.779036i
$698$		0			0
$699$	−29.6334	−	21.5299i	−1.12084	−	0.814337i
$700$		0			0
$701$	12.2949	+	37.8398i	0.464372	+	1.42919i	0.859771	+	0.510680i	$0.170606\pi$
$701$	12.2949	+	37.8398i	0.464372	+	1.42919i	−0.395399	+	0.918509i	$0.629394\pi$
$702$		0			0
$703$	−0.399684			−0.0150744
$704$		0			0
$705$	−32.8136			−1.23583
$706$		0			0
$707$	0.174825	+	0.538058i	0.00657499	+	0.0202357i
$708$		0			0
$709$	39.5351	+	28.7239i	1.48477	+	1.07875i	0.975980	+	0.217861i	$0.0699081\pi$
$709$	39.5351	+	28.7239i	1.48477	+	1.07875i	0.508793	+	0.860889i	$0.330092\pi$
$710$		0			0
$711$	28.8291	−	88.7268i	1.08118	−	3.32751i
$712$		0			0
$713$	0.571652	−	0.415330i	0.0214085	−	0.0155542i
$714$		0			0
$715$	3.54193	+	37.8496i	0.132461	+	1.41549i
$716$		0			0
$717$	46.3161	−	33.6506i	1.72971	−	1.25671i
$718$		0			0
$719$	−9.55235	+	29.3991i	−0.356242	+	1.09640i	0.599043	+	0.800717i	$0.295548\pi$
$719$	−9.55235	+	29.3991i	−0.356242	+	1.09640i	−0.955286	+	0.295685i	$0.904452\pi$
$720$		0			0
$721$	−3.86486	−	2.80798i	−0.143935	−	0.104575i
$722$		0			0
$723$	−8.89456	−	27.3746i	−0.330792	−	1.01807i
$724$		0			0
$725$	2.51528			0.0934153
$726$		0			0
$727$	−32.1977			−1.19415			−0.597074	−	0.802186i	$-0.703670\pi$
$727$	−32.1977			−1.19415			−0.597074	+	0.802186i	$0.703670\pi$
$728$		0			0
$729$	−12.0827	−	37.1866i	−0.447506	−	1.37728i
$730$		0			0
$731$	−17.2891	−	12.5613i	−0.639460	−	0.464595i
$732$		0			0
$733$	8.99064	−	27.6703i	0.332077	−	1.02203i	−0.636067	−	0.771633i	$-0.719440\pi$
$733$	8.99064	−	27.6703i	0.332077	−	1.02203i	0.968144	−	0.250394i	$-0.0805600\pi$
$734$		0			0
$735$	−39.7722	+	28.8962i	−1.46702	+	1.06585i
$736$		0			0
$737$	−3.84617	−	41.1007i	−0.141676	−	1.51396i
$738$		0			0
$739$	−25.9035	+	18.8200i	−0.952876	+	0.692305i	−0.951485	−	0.307694i	$-0.900443\pi$
$739$	−25.9035	+	18.8200i	−0.952876	+	0.692305i	−0.00139086	+	0.999999i	$0.500443\pi$
$740$		0			0
$741$	−4.19984	+	12.9258i	−0.154285	+	0.474841i
$742$		0			0
$743$	−27.5600	−	20.0235i	−1.01108	−	0.734592i	−0.0466437	−	0.998912i	$-0.514853\pi$
$743$	−27.5600	−	20.0235i	−1.01108	−	0.734592i	−0.964435	+	0.264320i	$0.914853\pi$
$744$		0			0
$745$	−1.47334	−	4.53448i	−0.0539791	−	0.166131i
$746$		0			0
$747$	−36.9787			−1.35298
$748$		0			0
$749$	2.88080			0.105262
$750$		0			0
$751$	9.59095	+	29.5179i	0.349979	+	1.07712i	0.958864	+	0.283865i	$0.0916168\pi$
$751$	9.59095	+	29.5179i	0.349979	+	1.07712i	−0.608886	+	0.793258i	$0.708383\pi$
$752$		0			0
$753$	−49.2447	−	35.7784i	−1.79458	−	1.30384i
$754$		0			0
$755$	−5.74817	+	17.6911i	−0.209197	+	0.643843i
$756$		0			0
$757$	30.6831	−	22.2926i	1.11520	−	0.810237i	0.131721	−	0.991287i	$-0.457950\pi$
$757$	30.6831	−	22.2926i	1.11520	−	0.810237i	0.983474	+	0.181050i	$0.0579496\pi$
$758$		0			0
$759$	6.58964	−	2.84424i	0.239189	−	0.103239i
$760$		0			0
$761$	10.1833	−	7.39861i	0.369145	−	0.268199i	−0.387711	−	0.921781i	$-0.626734\pi$
$761$	10.1833	−	7.39861i	0.369145	−	0.268199i	0.756856	+	0.653581i	$0.226734\pi$
$762$		0			0
$763$	0.644265	−	1.98284i	0.0233240	−	0.0717838i
$764$		0			0
$765$	27.1845	+	19.7507i	0.982857	+	0.714088i
$766$		0			0
$767$	−18.3932	−	56.6085i	−0.664140	−	2.04401i
$768$		0			0
$769$	−41.2934			−1.48908			−0.744540	−	0.667578i	$-0.767331\pi$
$769$	−41.2934			−1.48908			−0.744540	+	0.667578i	$0.767331\pi$
$770$		0			0
$771$	−33.8774			−1.22006
$772$		0			0
$773$	4.51180	+	13.8859i	0.162278	+	0.499441i	0.998825	−	0.0484540i	$-0.0154294\pi$
$773$	4.51180	+	13.8859i	0.162278	+	0.499441i	−0.836547	+	0.547895i	$0.815429\pi$
$774$		0			0
$775$	0.745819	+	0.541869i	0.0267906	+	0.0194645i
$776$		0			0
$777$	−0.0877745	+	0.270142i	−0.00314889	+	0.00969130i
$778$		0			0
$779$	6.87177	−	4.99264i	0.246207	−	0.178880i
$780$		0			0
$781$	−18.1857	+	30.6844i	−0.650735	+	1.09797i
$782$		0			0
$783$	14.5277	−	10.5550i	0.519179	−	0.377206i
$784$		0			0
$785$	−0.562368	+	1.73079i	−0.0200718	+	0.0617746i
$786$		0			0
$787$	−38.7976	−	28.1881i	−1.38299	−	1.00480i	−0.996594	−	0.0824641i	$-0.973721\pi$
$787$	−38.7976	−	28.1881i	−1.38299	−	1.00480i	−0.386393	−	0.922334i	$-0.626279\pi$
$788$		0			0
$789$	19.9143	+	61.2899i	0.708968	+	2.18198i
$790$		0			0
$791$	−0.560348			−0.0199237
$792$		0			0
$793$	−19.3200			−0.686072
$794$		0			0
$795$	−16.9841	−	52.2718i	−0.602366	−	1.85389i
$796$		0			0
$797$	18.5296	+	13.4625i	0.656351	+	0.476867i	0.865429	−	0.501032i	$-0.167046\pi$
$797$	18.5296	+	13.4625i	0.656351	+	0.476867i	−0.209078	+	0.977899i	$0.567046\pi$
$798$		0			0
$799$	−3.64438	+	11.2162i	−0.128929	+	0.396802i
$800$		0			0
$801$	−59.1543	+	42.9781i	−2.09012	+	1.51856i
$802$		0			0
$803$	17.2062	+	3.86303i	0.607193	+	0.136323i
$804$		0			0
$805$	0.362046	−	0.263042i	0.0127605	−	0.00927101i
$806$		0			0
$807$	2.21648	−	6.82163i	0.0780239	−	0.240133i
$808$		0			0
$809$	−33.0158	−	23.9874i	−1.16077	−	0.843351i	−0.170898	−	0.985289i	$-0.554667\pi$
$809$	−33.0158	−	23.9874i	−1.16077	−	0.843351i	−0.989876	+	0.141937i	$0.954667\pi$
$810$		0			0
$811$	6.50298	+	20.0141i	0.228351	+	0.702791i	0.997934	+	0.0642448i	$0.0204638\pi$
$811$	6.50298	+	20.0141i	0.228351	+	0.702791i	−0.769584	+	0.638546i	$0.779536\pi$
$812$		0			0
$813$	−47.7806			−1.67574
$814$		0			0
$815$	−0.831084			−0.0291116
$816$		0			0
$817$	−2.59382	−	7.98296i	−0.0907463	−	0.279288i
$818$		0			0
$819$	5.02322	+	3.64959i	0.175526	+	0.127527i
$820$		0			0
$821$	0.401692	−	1.23628i	0.0140192	−	0.0431465i	−0.943802	−	0.330511i	$-0.892779\pi$
$821$	0.401692	−	1.23628i	0.0140192	−	0.0431465i	0.957821	+	0.287364i	$0.0927790\pi$
$822$		0			0
$823$	10.7280	−	7.79432i	0.373953	−	0.271693i	−0.384895	−	0.922960i	$-0.625762\pi$
$823$	10.7280	−	7.79432i	0.373953	−	0.271693i	0.758848	+	0.651267i	$0.225762\pi$
$824$		0			0
$825$	6.18590	+	7.02984i	0.215365	+	0.244748i
$826$		0			0
$827$	−9.33734	+	6.78398i	−0.324691	+	0.235902i	−0.738175	−	0.674610i	$-0.764312\pi$
$827$	−9.33734	+	6.78398i	−0.324691	+	0.235902i	0.413483	+	0.910512i	$0.364312\pi$
$828$		0			0
$829$	1.61566	−	4.97248i	0.0561141	−	0.172701i	−0.919071	−	0.394091i	$-0.871059\pi$
$829$	1.61566	−	4.97248i	0.0561141	−	0.172701i	0.975185	+	0.221390i	$0.0710593\pi$
$830$		0			0
$831$	26.1916	+	19.0293i	0.908575	+	0.660118i
$832$		0			0
$833$	5.45997	+	16.8041i	0.189177	+	0.582226i
$834$		0			0
$835$	23.7797			0.822932
$836$		0			0
$837$	6.58157			0.227492
$838$		0			0
$839$	−11.2800	−	34.7164i	−0.389430	−	1.19854i	−0.933215	−	0.359317i	$-0.883010\pi$
$839$	−11.2800	−	34.7164i	−0.389430	−	1.19854i	0.543786	−	0.839224i	$-0.316990\pi$
$840$		0			0
$841$	18.0680	+	13.1272i	0.623036	+	0.452662i
$842$		0			0
$843$	−5.22018	+	16.0661i	−0.179792	+	0.553344i
$844$		0			0
$845$	−17.7782	+	12.9166i	−0.611589	+	0.444345i
$846$		0			0
$847$	0.343094	−	2.67540i	0.0117889	−	0.0919277i
$848$		0			0
$849$	1.47011	−	1.06809i	0.0504539	−	0.0366569i
$850$		0			0
$851$	−0.0922210	+	0.283827i	−0.00316130	+	0.00972947i
$852$		0			0
$853$	−11.8535	−	8.61208i	−0.405857	−	0.294872i	0.366066	−	0.930589i	$-0.380705\pi$
$853$	−11.8535	−	8.61208i	−0.405857	−	0.294872i	−0.771922	+	0.635717i	$0.780705\pi$
$854$		0			0
$855$	4.07840	+	12.5520i	0.139478	+	0.429270i
$856$		0			0
$857$	−40.3772			−1.37926			−0.689630	−	0.724162i	$-0.742227\pi$
$857$	−40.3772			−1.37926			−0.689630	+	0.724162i	$0.742227\pi$
$858$		0			0
$859$	−4.57561			−0.156118			−0.0780589	−	0.996949i	$-0.524872\pi$
$859$	−4.57561			−0.156118			−0.0780589	+	0.996949i	$0.524872\pi$
$860$		0			0
$861$	−1.86536	−	5.74098i	−0.0635713	−	0.195652i
$862$		0			0
$863$	−7.58174	−	5.50845i	−0.258085	−	0.187510i	0.451217	−	0.892414i	$-0.350990\pi$
$863$	−7.58174	−	5.50845i	−0.258085	−	0.187510i	−0.709302	+	0.704904i	$0.750990\pi$
$864$		0			0
$865$	−9.88252	+	30.4153i	−0.336016	+	1.03415i
$866$		0			0
$867$	−24.6615	+	17.9176i	−0.837549	+	0.608515i
$868$		0			0
$869$	−37.8546	−	43.0191i	−1.28413	−	1.45932i
$870$		0			0
$871$	47.2197	−	34.3071i	1.59998	−	1.16245i
$872$		0			0
$873$	−5.66462	+	17.4339i	−0.191719	+	0.590049i
$874$		0			0
$875$	−1.95204	−	1.41824i	−0.0659911	−	0.0479454i
$876$		0			0
$877$	14.2413	+	43.8301i	0.480893	+	1.48004i	0.837842	+	0.545913i	$0.183817\pi$
$877$	14.2413	+	43.8301i	0.480893	+	1.48004i	−0.356949	+	0.934124i	$0.616183\pi$
$878$		0			0
$879$	−28.2460			−0.952715
$880$		0			0
$881$	−37.4304			−1.26106			−0.630532	−	0.776163i	$-0.717163\pi$
$881$	−37.4304			−1.26106			−0.630532	+	0.776163i	$0.717163\pi$
$882$		0			0
$883$	9.07163	+	27.9196i	0.305285	+	0.939569i	0.979571	+	0.201099i	$0.0644514\pi$
$883$	9.07163	+	27.9196i	0.305285	+	0.939569i	−0.674286	+	0.738470i	$0.735549\pi$
$884$		0			0
$885$	−72.7417	−	52.8500i	−2.44519	−	1.77653i
$886$		0			0
$887$	7.68105	−	23.6398i	0.257904	−	0.793748i	−0.735339	−	0.677699i	$-0.762977\pi$
$887$	7.68105	−	23.6398i	0.257904	−	0.793748i	0.993244	−	0.116049i	$-0.0370228\pi$
$888$		0			0
$889$	1.76055	−	1.27911i	0.0590470	−	0.0429001i
$890$		0			0
$891$	12.8069	+	2.87532i	0.429046	+	0.0963268i
$892$		0			0
$893$	−3.74750	+	2.72272i	−0.125405	+	0.0911123i
$894$		0			0
$895$	14.9108	−	45.8908i	0.498413	−	1.53396i
$896$		0			0
$897$	8.20992	+	5.96485i	0.274121	+	0.199161i
$898$		0			0
$899$	−0.755059	−	2.32383i	−0.0251826	−	0.0775041i
$900$		0			0
$901$	−19.7537			−0.658090
$902$		0			0
$903$	−5.96522			−0.198510
$904$		0			0
$905$	17.2488	+	53.0863i	0.573369	+	1.76465i
$906$		0			0
$907$	−31.6035	−	22.9613i	−1.04938	−	0.762416i	−0.0772824	−	0.997009i	$-0.524624\pi$
$907$	−31.6035	−	22.9613i	−1.04938	−	0.762416i	−0.972094	+	0.234593i	$0.924624\pi$
$908$		0			0
$909$	−3.84978	+	11.8484i	−0.127689	+	0.392987i
$910$		0			0
$911$	19.6743	−	14.2942i	0.651839	−	0.473589i	−0.212058	−	0.977257i	$-0.568017\pi$
$911$	19.6743	−	14.2942i	0.651839	−	0.473589i	0.863897	+	0.503668i	$0.168017\pi$
$912$		0			0
$913$	−11.5804	+	19.5394i	−0.383254	+	0.646659i
$914$		0			0
$915$	−23.6110	+	17.1544i	−0.780556	+	0.567107i
$916$		0			0
$917$	−0.116520	+	0.358612i	−0.00384783	+	0.0118424i
$918$		0			0
$919$	−4.33416	−	3.14895i	−0.142971	−	0.103874i	0.514001	−	0.857790i	$-0.328163\pi$
$919$	−4.33416	−	3.14895i	−0.142971	−	0.103874i	−0.656972	+	0.753915i	$0.728163\pi$
$920$		0			0
$921$	−22.3515	−	68.7910i	−0.736508	−	2.26674i
$922$		0			0
$923$	−50.4324			−1.66000
$924$		0			0
$925$	−0.389358			−0.0128020
$926$		0			0
$927$	−32.5079	−	100.049i	−1.06770	−	3.28604i
$928$		0			0
$929$	46.0380	+	33.4486i	1.51046	+	1.09741i	0.965973	+	0.258642i	$0.0832751\pi$
$929$	46.0380	+	33.4486i	1.51046	+	1.09741i	0.544486	+	0.838770i	$0.316725\pi$
$930$		0			0
$931$	−2.14454	+	6.60021i	−0.0702844	+	0.216313i
$932$		0			0
$933$	−24.3668	+	17.7035i	−0.797732	+	0.579586i
$934$		0			0
$935$	18.9494	−	8.17897i	0.619710	−	0.267481i
$936$		0			0
$937$	16.7167	−	12.1454i	0.546110	−	0.396772i	−0.280240	−	0.959930i	$-0.590414\pi$
$937$	16.7167	−	12.1454i	0.546110	−	0.396772i	0.826349	+	0.563158i	$0.190414\pi$
$938$		0			0
$939$	22.5817	−	69.4992i	0.736925	−	2.26802i
$940$		0			0
$941$	−21.8030	−	15.8408i	−0.710757	−	0.516395i	0.172661	−	0.984981i	$-0.444763\pi$
$941$	−21.8030	−	15.8408i	−0.710757	−	0.516395i	−0.883418	+	0.468586i	$0.844763\pi$
$942$		0			0
$943$	−1.95986	−	6.03181i	−0.0638217	−	0.196423i
$944$		0			0
$945$	4.16833			0.135596
$946$		0			0
$947$	43.3235			1.40782			0.703912	−	0.710287i	$-0.251435\pi$
$947$	43.3235			1.40782			0.703912	+	0.710287i	$0.251435\pi$
$948$		0			0
$949$	7.70492	+	23.7133i	0.250112	+	0.769767i
$950$		0			0
$951$	25.4221	+	18.4702i	0.824368	+	0.598939i
$952$		0			0
$953$	6.94336	−	21.3695i	0.224918	−	0.692225i	−0.773382	−	0.633940i	$-0.781437\pi$
$953$	6.94336	−	21.3695i	0.224918	−	0.692225i	0.998300	−	0.0582852i	$-0.0185633\pi$
$954$		0			0
$955$	28.9177	−	21.0099i	0.935753	−	0.679864i
$956$		0			0
$957$	−2.31243	−	24.7109i	−0.0747502	−	0.798791i
$958$		0			0
$959$	−0.167815	+	0.121925i	−0.00541903	+	0.00393715i
$960$		0			0
$961$	−9.30279	+	28.6310i	−0.300090	+	0.923582i
$962$		0			0
$963$	51.3218	+	37.2875i	1.65382	+	1.20157i
$964$		0			0
$965$	14.8842	+	45.8089i	0.479140	+	1.47464i
$966$		0			0
$967$	−9.03749			−0.290626			−0.145313	−	0.989386i	$-0.546419\pi$
$967$	−9.03749			−0.290626			−0.145313	+	0.989386i	$0.546419\pi$
$968$		0			0
$969$	7.37884			0.237042
$970$		0			0
$971$	0.306047	+	0.941916i	0.00982152	+	0.0302275i	0.955847	−	0.293864i	$-0.0949413\pi$
$971$	0.306047	+	0.941916i	0.00982152	+	0.0302275i	−0.946026	+	0.324092i	$0.894941\pi$
$972$		0			0
$973$	−1.02050	−	0.741437i	−0.0327157	−	0.0237694i
$974$		0			0
$975$	−4.09134	+	12.5918i	−0.131028	+	0.403262i
$976$		0			0
$977$	15.7123	−	11.4157i	0.502682	−	0.365220i	−0.307358	−	0.951594i	$-0.599445\pi$
$977$	15.7123	−	11.4157i	0.502682	−	0.365220i	0.810041	+	0.586374i	$0.199445\pi$
$978$		0			0
$979$	4.18449	+	44.7161i	0.133737	+	1.42913i
$980$		0			0
$981$	37.1425	−	26.9856i	1.18587	−	0.861583i
$982$		0			0
$983$	−0.777006	+	2.39138i	−0.0247826	+	0.0762731i	−0.962683	−	0.270632i	$-0.912767\pi$
$983$	−0.777006	+	2.39138i	−0.0247826	+	0.0762731i	0.937900	+	0.346905i	$0.112767\pi$
$984$		0			0
$985$	20.1726	+	14.6562i	0.642751	+	0.466986i
$986$		0			0
$987$	1.01727	+	3.13083i	0.0323800	+	0.0996554i
$988$		0			0
$989$	−6.26741			−0.199292
$990$		0			0
$991$	21.0983			0.670210			0.335105	−	0.942181i	$-0.391228\pi$
$991$	21.0983			0.670210			0.335105	+	0.942181i	$0.391228\pi$
$992$		0			0
$993$	22.0912	+	67.9897i	0.701043	+	2.15759i
$994$		0			0
$995$	4.40659	+	3.20158i	0.139698	+	0.101497i
$996$		0			0
$997$	−9.79701	+	30.1521i	−0.310274	+	0.954927i	0.667382	+	0.744716i	$0.267415\pi$
$997$	−9.79701	+	30.1521i	−0.310274	+	0.954927i	−0.977656	+	0.210211i	$0.932585\pi$
$998$		0			0
$999$	−2.24885	+	1.63388i	−0.0711505	+	0.0516938i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	836.2.j.a.685.1	yes	12
11.2	odd	10		9196.2.a.i.1.1		6
11.4	even	5	inner	836.2.j.a.609.1	✓	12
11.9	even	5		9196.2.a.j.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
836.2.j.a.609.1	✓	12	11.4	even	5	inner
836.2.j.a.685.1	yes	12	1.1	even	1	trivial
9196.2.a.i.1.1		6	11.2	odd	10
9196.2.a.j.1.1		6	11.9	even	5

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:	\( N \)	\(=\)	\( 836 = 2^{2} \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	836.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.895600 - 2.75637i) q^{3} +(-1.97741 - 1.43667i) q^{5} +(-0.0757739 + 0.233208i) q^{7} +(-4.36844 + 3.17385i) q^{9} +(0.309017 + 3.30220i) q^{11} +(-3.79382 + 2.75637i) q^{13} +(-2.18903 + 6.73715i) q^{15} +(2.05975 + 1.49650i) q^{17} +(0.309017 + 0.951057i) q^{19} +0.710671 q^{21} +0.746673 q^{23} +(0.301033 + 0.926485i) q^{25} +(5.62656 + 4.08794i) q^{27} +(0.797879 - 2.45562i) q^{29} +(0.765599 - 0.556240i) q^{31} +(8.82533 - 3.80921i) q^{33} +(0.484879 - 0.352285i) q^{35} +(-0.123509 + 0.380122i) q^{37} +(10.9953 + 7.98857i) q^{39} +(-2.62478 - 8.07825i) q^{41} -8.39378 q^{43} +13.1980 q^{45} +(1.43142 + 4.40545i) q^{47} +(5.61447 + 4.07915i) q^{49} +(2.28019 - 7.01769i) q^{51} +(-6.27695 + 4.56047i) q^{53} +(4.13312 - 6.97375i) q^{55} +(2.34471 - 1.70353i) q^{57} +(-3.92228 + 12.0715i) q^{59} +(3.33307 + 2.42162i) q^{61} +(-0.409155 - 1.25925i) q^{63} +11.4619 q^{65} -12.4465 q^{67} +(-0.668720 - 2.05811i) q^{69} +(8.70057 + 6.32133i) q^{71} +(1.64304 - 5.05677i) q^{73} +(2.28413 - 1.65952i) q^{75} +(-0.793515 - 0.178155i) q^{77} +(-13.9778 + 10.1554i) q^{79} +(1.22295 - 3.76384i) q^{81} +(5.54039 + 4.02533i) q^{83} +(-1.92299 - 5.91836i) q^{85} -7.48318 q^{87} +13.5413 q^{89} +(-0.355336 - 1.09361i) q^{91} +(-2.21888 - 1.61211i) q^{93} +(0.755303 - 2.32458i) q^{95} +(2.74649 - 1.99544i) q^{97} +(-11.8306 - 13.4447i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{3} + q^{5} - 2 q^{7} - 8 q^{9} - 3 q^{11} - 3 q^{13} - 6 q^{15} + 7 q^{17} - 3 q^{19} + 10 q^{21} - 24 q^{23} - 16 q^{25} + q^{27} - 11 q^{29} + 14 q^{31} + q^{33} + 8 q^{35} - 17 q^{37} + 41 q^{39}+ \cdots - 28 q^{99}+O(q^{100}) \) 12 * q + q^3 + q^5 - 2 * q^7 - 8 * q^9 - 3 * q^11 - 3 * q^13 - 6 * q^15 + 7 * q^17 - 3 * q^19 + 10 * q^21 - 24 * q^23 - 16 * q^25 + q^27 - 11 * q^29 + 14 * q^31 + q^33 + 8 * q^35 - 17 * q^37 + 41 * q^39 + 10 * q^41 - 46 * q^43 + 16 * q^45 + 5 * q^47 - 5 * q^49 + 10 * q^51 - 8 * q^53 - 34 * q^55 + q^57 - 19 * q^59 + 36 * q^61 + 12 * q^63 + 28 * q^65 - 22 * q^67 - 10 * q^69 - 22 * q^71 + 12 * q^73 + 35 * q^75 + 8 * q^77 - 42 * q^79 - q^81 + 16 * q^83 + 19 * q^85 - 36 * q^87 + 26 * q^89 - 5 * q^91 + 34 * q^93 + 6 * q^95 + 34 * q^97 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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