LMFDB - Embedded newform 132.2.p.a.29.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [132,2,Mod(17,132)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(132, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("132.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 132 = 2^{2} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	132.p (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.05402530668$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 8 x^{14} - 12 x^{13} + 23 x^{12} - 72 x^{11} + 146 x^{10} - 176 x^{9} + 223 x^{8} + \cdots + 6561 $ x^16 - 4x^15 + 8x^14 - 12x^13 + 23x^12 - 72x^11 + 146x^10 - 176x^9 + 223x^8 - 528x^7 + 1314x^6 - 1944x^5 + 1863x^4 - 2916x^3 + 5832x^2 - 8748*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.4
Root			$-1.12228 - 1.31928i$ of defining polynomial
Character	$\chi$	$=$	132.29
Dual form			132.2.p.a.41.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.60151 + 0.659669i) q^{3} +(-1.45030 - 1.99617i) q^{5} +(3.40640 - 1.10681i) q^{7} +(2.12967 + 2.11293i) q^{9} +(-2.38857 + 2.30103i) q^{11} +(-2.28837 + 3.14966i) q^{13} +(-1.00586 - 4.15361i) q^{15} +(-0.938264 + 0.681689i) q^{17} +(-5.03232 - 1.63510i) q^{19} +(6.18551 + 0.474534i) q^{21} -7.11355i q^{23} +(-0.336235 + 1.03483i) q^{25} +(2.01686 + 4.78877i) q^{27} +(0.775461 + 2.38662i) q^{29} +(-4.08293 - 2.96642i) q^{31} +(-5.34324 + 2.10946i) q^{33} +(-7.14969 - 5.19455i) q^{35} +(-0.123555 - 0.380264i) q^{37} +(-5.74258 + 3.53466i) q^{39} +(-3.48049 + 10.7118i) q^{41} +1.31310i q^{43} +(1.12911 - 7.31559i) q^{45} +(5.67347 + 1.84342i) q^{47} +(4.71542 - 3.42595i) q^{49} +(-1.95233 + 0.472788i) q^{51} +(1.57118 - 2.16254i) q^{53} +(8.05740 + 1.43080i) q^{55} +(-6.98069 - 5.93830i) q^{57} +(11.7221 - 3.80874i) q^{59} +(4.67521 + 6.43487i) q^{61} +(9.59313 + 4.84036i) q^{63} +9.60609 q^{65} -3.87535 q^{67} +(4.69259 - 11.3924i) q^{69} +(-1.89329 - 2.60589i) q^{71} +(-4.98614 + 1.62010i) q^{73} +(-1.22113 + 1.43548i) q^{75} +(-5.58962 + 10.4819i) q^{77} +(8.63038 - 11.8787i) q^{79} +(0.0710170 + 8.99972i) q^{81} +(-2.92652 + 2.12624i) q^{83} +(2.72153 + 0.884280i) q^{85} +(-0.332473 + 4.33375i) q^{87} -12.1910i q^{89} +(-4.30902 + 13.2618i) q^{91} +(-4.58200 - 7.44414i) q^{93} +(4.03445 + 12.4168i) q^{95} +(-2.49831 - 1.81513i) q^{97} +(-9.94880 - 0.146440i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{3} + 5 q^{9} + 9 q^{15} - 30 q^{19} - 12 q^{25} + q^{27} - 10 q^{31} - 41 q^{33} - 24 q^{37} - 35 q^{39} + 2 q^{45} + 12 q^{49} - 15 q^{51} + 62 q^{55} + 35 q^{57} + 40 q^{61} + 55 q^{63} + 44 q^{67}+ \cdots - 101 q^{99}+O(q^{100}) $ 16 * q + q^3 + 5 * q^9 + 9 * q^15 - 30 * q^19 - 12 * q^25 + q^27 - 10 * q^31 - 41 * q^33 - 24 * q^37 - 35 * q^39 + 2 * q^45 + 12 * q^49 - 15 * q^51 + 62 * q^55 + 35 * q^57 + 40 * q^61 + 55 * q^63 + 44 * q^67 + 46 * q^69 + 10 * q^73 + 21 * q^75 + 20 * q^79 + 57 * q^81 - 60 * q^85 - 60 * q^91 + 7 * q^93 - 36 * q^97 - 101 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/132\mathbb{Z}\right)^\times$.

$n$	$13$	$67$	$89$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.60151	+	0.659669i	0.924633	+	0.380860i
$3$	1.60151	+	0.659669i	0.924633	+	0.380860i
$4$		0			0
$5$	−1.45030	−	1.99617i	−0.648595	−	0.892715i	0.350442	−	0.936584i	$-0.386031\pi$
$5$	−1.45030	−	1.99617i	−0.648595	−	0.892715i	−0.999037	+	0.0438695i	$0.986031\pi$
$6$		0			0
$7$	3.40640	−	1.10681i	1.28750	−	0.418333i	0.416283	−	0.909235i	$-0.363333\pi$
$7$	3.40640	−	1.10681i	1.28750	−	0.418333i	0.871215	+	0.490902i	$0.163333\pi$
$8$		0			0
$9$	2.12967	+	2.11293i	0.709891	+	0.704311i
$10$		0			0
$11$	−2.38857	+	2.30103i	−0.720180	+	0.693787i
$11$	−2.38857	+	2.30103i	−0.720180	+	0.693787i
$12$		0			0
$13$	−2.28837	+	3.14966i	−0.634678	+	0.873560i	−0.998318	−	0.0579800i	$-0.981534\pi$
$13$	−2.28837	+	3.14966i	−0.634678	+	0.873560i	0.363639	+	0.931540i	$0.381534\pi$
$14$		0			0
$15$	−1.00586	−	4.15361i	−0.259713	−	1.07246i
$16$		0			0
$17$	−0.938264	+	0.681689i	−0.227562	+	0.165334i	−0.695724	−	0.718309i	$-0.744916\pi$
$17$	−0.938264	+	0.681689i	−0.227562	+	0.165334i	0.468162	+	0.883643i	$0.344916\pi$
$18$		0			0
$19$	−5.03232	−	1.63510i	−1.15449	−	0.375118i	−0.331659	−	0.943399i	$-0.607608\pi$
$19$	−5.03232	−	1.63510i	−1.15449	−	0.375118i	−0.822834	+	0.568281i	$0.807608\pi$
$20$		0			0
$21$	6.18551	+	0.474534i	1.34979	+	0.103552i
$22$		0			0
$23$		−	7.11355i		−	1.48328i	−0.670799	−	0.741639i	$-0.734049\pi$
$23$		−	7.11355i		−	1.48328i	0.670799	−	0.741639i	$-0.265951\pi$
$24$		0			0
$25$	−0.336235	+	1.03483i	−0.0672470	+	0.206965i
$26$		0			0
$27$	2.01686	+	4.78877i	0.388144	+	0.921599i
$28$		0			0
$29$	0.775461	+	2.38662i	0.143999	+	0.443185i	0.996881	−	0.0789198i	$-0.0251471\pi$
$29$	0.775461	+	2.38662i	0.143999	+	0.443185i	−0.852882	+	0.522104i	$0.825147\pi$
$30$		0			0
$31$	−4.08293	−	2.96642i	−0.733315	−	0.532785i	0.157295	−	0.987552i	$-0.449723\pi$
$31$	−4.08293	−	2.96642i	−0.733315	−	0.532785i	−0.890611	+	0.454767i	$0.849723\pi$
$32$		0			0
$33$	−5.34324	+	2.10946i	−0.930138	+	0.367210i
$34$		0			0
$35$	−7.14969	−	5.19455i	−1.20852	−	0.878039i
$36$		0			0
$37$	−0.123555	−	0.380264i	−0.0203123	−	0.0625150i	0.940387	−	0.340108i	$-0.110463\pi$
$37$	−0.123555	−	0.380264i	−0.0203123	−	0.0625150i	−0.960699	+	0.277593i	$0.910463\pi$
$38$		0			0
$39$	−5.74258	+	3.53466i	−0.919548	+	0.565998i
$40$		0			0
$41$	−3.48049	+	10.7118i	−0.543561	+	1.67291i	0.180827	+	0.983515i	$0.442122\pi$
$41$	−3.48049	+	10.7118i	−0.543561	+	1.67291i	−0.724388	+	0.689392i	$0.757878\pi$
$42$		0			0
$43$			1.31310i			0.200246i	0.994975	+	0.100123i	$0.0319236\pi$
$43$			1.31310i			0.200246i	−0.994975	+	0.100123i	$0.968076\pi$
$44$		0			0
$45$	1.12911	−	7.31559i	0.168317	−	1.09054i
$46$		0			0
$47$	5.67347	+	1.84342i	0.827561	+	0.268891i	0.692018	−	0.721881i	$-0.256722\pi$
$47$	5.67347	+	1.84342i	0.827561	+	0.268891i	0.135543	+	0.990771i	$0.456722\pi$
$48$		0			0
$49$	4.71542	−	3.42595i	0.673631	−	0.489421i
$50$		0			0
$51$	−1.95233	+	0.472788i	−0.273381	+	0.0662035i
$52$		0			0
$53$	1.57118	−	2.16254i	0.215818	−	0.297048i	−0.687358	−	0.726319i	$-0.741229\pi$
$53$	1.57118	−	2.16254i	0.215818	−	0.297048i	0.903176	+	0.429271i	$0.141229\pi$
$54$		0			0
$55$	8.05740	+	1.43080i	1.08646	+	0.192928i
$56$		0			0
$57$	−6.98069	−	5.93830i	−0.924615	−	0.786547i
$58$		0			0
$59$	11.7221	−	3.80874i	1.52609	−	0.495855i	0.578589	−	0.815619i	$-0.303604\pi$
$59$	11.7221	−	3.80874i	1.52609	−	0.495855i	0.947497	+	0.319764i	$0.103604\pi$
$60$		0			0
$61$	4.67521	+	6.43487i	0.598599	+	0.823901i	0.995579	−	0.0939265i	$-0.0299419\pi$
$61$	4.67521	+	6.43487i	0.598599	+	0.823901i	−0.396980	+	0.917827i	$0.629942\pi$
$62$		0			0
$63$	9.59313	+	4.84036i	1.20862	+	0.609828i
$64$		0			0
$65$	9.60609			1.19149
$66$		0			0
$67$	−3.87535			−0.473449			−0.236725	−	0.971577i	$-0.576074\pi$
$67$	−3.87535			−0.473449			−0.236725	+	0.971577i	$0.576074\pi$
$68$		0			0
$69$	4.69259	−	11.3924i	0.564921	−	1.37149i
$70$		0			0
$71$	−1.89329	−	2.60589i	−0.224692	−	0.309262i	0.681756	−	0.731580i	$-0.261217\pi$
$71$	−1.89329	−	2.60589i	−0.224692	−	0.309262i	−0.906448	+	0.422317i	$0.861217\pi$
$72$		0			0
$73$	−4.98614	+	1.62010i	−0.583584	+	0.189618i	−0.585905	−	0.810379i	$-0.699261\pi$
$73$	−4.98614	+	1.62010i	−0.583584	+	0.189618i	0.00232161	+	0.999997i	$0.499261\pi$
$74$		0			0
$75$	−1.22113	+	1.43548i	−0.141004	+	0.165755i
$76$		0			0
$77$	−5.58962	+	10.4819i	−0.636996	+	1.19452i
$78$		0			0
$79$	8.63038	−	11.8787i	0.970994	−	1.33646i	0.0294502	−	0.999566i	$-0.490624\pi$
$79$	8.63038	−	11.8787i	0.970994	−	1.33646i	0.941543	−	0.336892i	$-0.109376\pi$
$80$		0			0
$81$	0.0710170	+	8.99972i	0.00789078	+	0.999969i
$82$		0			0
$83$	−2.92652	+	2.12624i	−0.321227	+	0.233385i	−0.736699	−	0.676221i	$-0.763617\pi$
$83$	−2.92652	+	2.12624i	−0.321227	+	0.233385i	0.415472	+	0.909606i	$0.363617\pi$
$84$		0			0
$85$	2.72153	+	0.884280i	0.295192	+	0.0959136i
$86$		0			0
$87$	−0.332473	+	4.33375i	−0.0356448	+	0.464627i
$88$		0			0
$89$		−	12.1910i		−	1.29225i	−0.763234	−	0.646123i	$-0.776389\pi$
$89$		−	12.1910i		−	1.29225i	0.763234	−	0.646123i	$-0.223611\pi$
$90$		0			0
$91$	−4.30902	+	13.2618i	−0.451708	+	1.39021i
$92$		0			0
$93$	−4.58200	−	7.44414i	−0.475131	−	0.771921i
$94$		0			0
$95$	4.03445	+	12.4168i	0.413926	+	1.27393i
$96$		0			0
$97$	−2.49831	−	1.81513i	−0.253665	−	0.184298i	0.453685	−	0.891162i	$-0.350109\pi$
$97$	−2.49831	−	1.81513i	−0.253665	−	0.184298i	−0.707349	+	0.706864i	$0.750109\pi$
$98$		0			0
$99$	−9.94880	−	0.146440i	−0.999892	−	0.0147177i
$100$		0			0
$101$	2.92652	+	2.12624i	0.291200	+	0.211569i	0.723788	−	0.690023i	$-0.242400\pi$
$101$	2.92652	+	2.12624i	0.291200	+	0.211569i	−0.432588	+	0.901592i	$0.642400\pi$
$102$		0			0
$103$	1.67101	+	5.14283i	0.164649	+	0.506738i	0.999010	−	0.0444801i	$-0.0141631\pi$
$103$	1.67101	+	5.14283i	0.164649	+	0.506738i	−0.834361	+	0.551218i	$0.814163\pi$
$104$		0			0
$105$	−8.02362	−	13.0356i	−0.783025	−	1.27214i
$106$		0			0
$107$	3.03750	−	9.34846i	0.293646	−	0.903749i	−0.690027	−	0.723784i	$-0.742401\pi$
$107$	3.03750	−	9.34846i	0.293646	−	0.903749i	0.983673	−	0.179966i	$-0.0575987\pi$
$108$		0			0
$109$		−	17.2330i		−	1.65062i	−0.564681	−	0.825310i	$-0.691001\pi$
$109$		−	17.2330i		−	1.65062i	0.564681	−	0.825310i	$-0.308999\pi$
$110$		0			0
$111$	0.0529733	−	0.690502i	0.00502800	−	0.0655395i
$112$		0			0
$113$	11.8430	+	3.84801i	1.11409	+	0.361991i	0.807510	−	0.589854i	$-0.200815\pi$
$113$	11.8430	+	3.84801i	1.11409	+	0.361991i	0.306582	+	0.951844i	$0.400815\pi$
$114$		0			0
$115$	−14.1999	+	10.3168i	−1.32414	+	0.962047i
$116$		0			0
$117$	−11.5285	+	1.87259i	−1.06581	+	0.173121i
$118$		0			0
$119$	−2.44160	+	3.36058i	−0.223821	+	0.308064i
$120$		0			0
$121$	0.410506	−	10.9923i	0.0373187	−	0.999303i
$122$		0			0
$123$	−12.6403	+	14.8591i	−1.13974	+	1.33980i
$124$		0			0
$125$	−9.17987	+	2.98272i	−0.821072	+	0.266783i
$126$		0			0
$127$	2.69400	+	3.70797i	0.239053	+	0.329029i	0.911640	−	0.410990i	$-0.134817\pi$
$127$	2.69400	+	3.70797i	0.239053	+	0.329029i	−0.672587	+	0.740018i	$0.734817\pi$
$128$		0			0
$129$	−0.866211	+	2.10294i	−0.0762656	+	0.185154i
$130$		0			0
$131$	9.77772			0.854284			0.427142	−	0.904185i	$-0.359520\pi$
$131$	9.77772			0.854284			0.427142	+	0.904185i	$0.359520\pi$
$132$		0			0
$133$	−18.9518			−1.64333
$134$		0			0
$135$	6.63414	−	10.9712i	0.570976	−	0.944247i
$136$		0			0
$137$	5.82713	+	8.02035i	0.497845	+	0.685225i	0.981811	−	0.189862i	$-0.0608041\pi$
$137$	5.82713	+	8.02035i	0.497845	+	0.685225i	−0.483966	+	0.875087i	$0.660804\pi$
$138$		0			0
$139$	10.0684	−	3.27143i	0.853993	−	0.277479i	0.150875	−	0.988553i	$-0.451791\pi$
$139$	10.0684	−	3.27143i	0.853993	−	0.277479i	0.703117	+	0.711074i	$0.251791\pi$
$140$		0			0
$141$	7.87008	+	6.69487i	0.662780	+	0.563810i
$142$		0			0
$143$	−1.78156	−	12.7888i	−0.148982	−	1.06945i
$144$		0			0
$145$	3.63945	−	5.00928i	0.302240	−	0.415998i
$146$		0			0
$147$	9.81178	−	2.37608i	0.809262	−	0.195976i
$148$		0			0
$149$	−6.46004	+	4.69349i	−0.529227	+	0.384506i	−0.820069	−	0.572265i	$-0.806065\pi$
$149$	−6.46004	+	4.69349i	−0.529227	+	0.384506i	0.290841	+	0.956771i	$0.406065\pi$
$150$		0			0
$151$	−8.01167	−	2.60315i	−0.651980	−	0.211841i	−0.0356933	−	0.999363i	$-0.511364\pi$
$151$	−8.01167	−	2.60315i	−0.651980	−	0.211841i	−0.616287	+	0.787522i	$0.711364\pi$
$152$		0			0
$153$	−3.43856	−	0.530716i	−0.277991	−	0.0429058i
$154$		0			0
$155$			12.4524i			1.00020i
$156$		0			0
$157$	−4.39155	+	13.5158i	−0.350483	+	1.07868i	0.608099	+	0.793861i	$0.291932\pi$
$157$	−4.39155	+	13.5158i	−0.350483	+	1.07868i	−0.958582	+	0.284816i	$0.908068\pi$
$158$		0			0
$159$	3.94282	−	2.42688i	0.312686	−	0.192464i
$160$		0			0
$161$	−7.87332	−	24.2316i	−0.620505	−	1.90972i
$162$		0			0
$163$	6.85233	+	4.97851i	0.536716	+	0.389947i	0.822864	−	0.568238i	$-0.192375\pi$
$163$	6.85233	+	4.97851i	0.536716	+	0.389947i	−0.286148	+	0.958185i	$0.592375\pi$
$164$		0			0
$165$	11.9602	+	7.60665i	0.931097	+	0.592177i
$166$		0			0
$167$	−13.7375	−	9.98086i	−1.06304	−	0.772342i	−0.0883895	−	0.996086i	$-0.528172\pi$
$167$	−13.7375	−	9.98086i	−1.06304	−	0.772342i	−0.974648	+	0.223744i	$0.928172\pi$
$168$		0			0
$169$	−0.666550	−	2.05143i	−0.0512731	−	0.157802i
$170$		0			0
$171$	−7.26234	−	14.1152i	−0.555365	−	1.07942i
$172$		0			0
$173$	−2.52546	+	7.77256i	−0.192007	+	0.590937i	0.807991	+	0.589194i	$0.200555\pi$
$173$	−2.52546	+	7.77256i	−0.192007	+	0.590937i	−0.999998	+	0.00174265i	$0.999445\pi$
$174$		0			0
$175$			3.89718i			0.294599i
$176$		0			0
$177$	21.2856	+	1.63297i	1.59992	+	0.122741i
$178$		0			0
$179$	−19.5207	−	6.34266i	−1.45905	−	0.474073i	−0.531268	−	0.847204i	$-0.678284\pi$
$179$	−19.5207	−	6.34266i	−1.45905	−	0.474073i	−0.927779	+	0.373131i	$0.878284\pi$
$180$		0			0
$181$	4.11147	−	2.98716i	0.305603	−	0.222034i	−0.424405	−	0.905473i	$-0.639517\pi$
$181$	4.11147	−	2.98716i	0.305603	−	0.222034i	0.730008	+	0.683439i	$0.239517\pi$
$182$		0			0
$183$	3.24251	+	13.3896i	0.239693	+	0.989788i
$184$		0			0
$185$	−0.579879	+	0.798135i	−0.0426335	+	0.0586800i
$186$		0			0
$187$	0.672519	−	3.78723i	0.0491795	−	0.276950i
$188$		0			0
$189$	12.1705	+	14.0802i	0.885271	+	1.02418i
$190$		0			0
$191$	−0.444200	+	0.144329i	−0.0321412	+	0.0104433i	−0.325043	−	0.945699i	$-0.605379\pi$
$191$	−0.444200	+	0.144329i	−0.0321412	+	0.0104433i	0.292902	+	0.956142i	$0.405379\pi$
$192$		0			0
$193$	13.5372	+	18.6324i	0.974429	+	1.34119i	0.939778	+	0.341787i	$0.111032\pi$
$193$	13.5372	+	18.6324i	0.974429	+	1.34119i	0.0346512	+	0.999399i	$0.488968\pi$
$194$		0			0
$195$	15.3843	+	6.33684i	1.10169	+	0.453791i
$196$		0			0
$197$	−15.8503			−1.12929			−0.564643	−	0.825335i	$-0.690986\pi$
$197$	−15.8503			−1.12929			−0.564643	+	0.825335i	$0.690986\pi$
$198$		0			0
$199$	12.3482			0.875342			0.437671	−	0.899135i	$-0.355803\pi$
$199$	12.3482			0.875342			0.437671	+	0.899135i	$0.355803\pi$
$200$		0			0
$201$	−6.20642	−	2.55645i	−0.437767	−	0.180318i
$202$		0			0
$203$	5.28306	+	7.27150i	0.370798	+	0.510360i
$204$		0			0
$205$	26.4304	−	8.58776i	1.84598	−	0.599795i
$206$		0			0
$207$	15.0305	−	15.1495i	1.04469	−	1.05297i
$208$		0			0
$209$	15.7825	−	7.67398i	1.09170	−	0.530821i
$210$		0			0
$211$	2.31691	−	3.18895i	0.159502	−	0.219536i	−0.721785	−	0.692118i	$-0.756678\pi$
$211$	2.31691	−	3.18895i	0.159502	−	0.219536i	0.881287	+	0.472582i	$0.156678\pi$
$212$		0			0
$213$	−1.31310	−	5.42231i	−0.0899721	−	0.371531i
$214$		0			0
$215$	2.62117	−	1.90439i	0.178762	−	0.129878i
$216$		0			0
$217$	−17.1913	−	5.58580i	−1.16702	−	0.379189i
$218$		0			0
$219$	−9.05409	−	0.694603i	−0.611819	−	0.0469369i
$220$		0			0
$221$		−	4.51517i		−	0.303723i
$222$		0			0
$223$	0.0354754	−	0.109182i	0.00237561	−	0.00731138i	−0.949862	−	0.312670i	$-0.898776\pi$
$223$	0.0354754	−	0.109182i	0.00237561	−	0.00731138i	0.952237	+	0.305359i	$0.0987765\pi$
$224$		0			0
$225$	−2.90259	+	1.49340i	−0.193506	+	0.0995598i
$226$		0			0
$227$	1.98139	+	6.09809i	0.131509	+	0.404744i	0.995031	−	0.0995679i	$-0.0317461\pi$
$227$	1.98139	+	6.09809i	0.131509	+	0.404744i	−0.863521	+	0.504312i	$0.831746\pi$
$228$		0			0
$229$	−15.2749	−	11.0979i	−1.00939	−	0.733368i	−0.0453123	−	0.998973i	$-0.514428\pi$
$229$	−15.2749	−	11.0979i	−1.00939	−	0.733368i	−0.964082	+	0.265605i	$0.914428\pi$
$230$		0			0
$231$	−15.8664	+	13.0996i	−1.04393	+	0.861890i
$232$		0			0
$233$	16.2469	+	11.8041i	1.06437	+	0.773311i	0.974892	−	0.222678i	$-0.0714799\pi$
$233$	16.2469	+	11.8041i	1.06437	+	0.773311i	0.0894787	+	0.995989i	$0.471480\pi$
$234$		0			0
$235$	−4.54847	−	13.9987i	−0.296709	−	0.913177i
$236$		0			0
$237$	21.6577	−	13.3307i	1.40682	−	0.865920i
$238$		0			0
$239$	5.00853	−	15.4147i	0.323975	−	0.997091i	−0.647927	−	0.761703i	$-0.724364\pi$
$239$	5.00853	−	15.4147i	0.323975	−	0.997091i	0.971901	−	0.235389i	$-0.0756363\pi$
$240$		0			0
$241$			18.1990i			1.17230i	0.810202	+	0.586150i	$0.199357\pi$
$241$			18.1990i			1.17230i	−0.810202	+	0.586150i	$0.800643\pi$
$242$		0			0
$243$	−5.82310	+	14.4600i	−0.373552	+	0.927609i
$244$		0			0
$245$	−13.6776	−	4.44411i	−0.873828	−	0.283924i
$246$		0			0
$247$	16.6658	−	12.1084i	1.06042	−	0.770440i
$248$		0			0
$249$	−6.08947	+	1.47466i	−0.385904	+	0.0934530i
$250$		0			0
$251$	−1.62300	+	2.23387i	−0.102443	+	0.141001i	−0.857161	−	0.515049i	$-0.827774\pi$
$251$	−1.62300	+	2.23387i	−0.102443	+	0.141001i	0.754718	+	0.656050i	$0.227774\pi$
$252$		0			0
$253$	16.3685	+	16.9912i	1.02908	+	1.06823i
$254$		0			0
$255$	3.77523	+	3.21150i	0.236414	+	0.201112i
$256$		0			0
$257$	−24.1449	+	7.84517i	−1.50612	+	0.489368i	−0.941796	−	0.336185i	$-0.890863\pi$
$257$	−24.1449	+	7.84517i	−1.50612	+	0.489368i	−0.564324	+	0.825553i	$0.690863\pi$
$258$		0			0
$259$	−0.841756	−	1.15858i	−0.0523042	−	0.0719905i
$260$		0			0
$261$	−3.39130	+	6.72122i	−0.209916	+	0.416033i
$262$		0			0
$263$	−21.5021			−1.32588			−0.662938	−	0.748674i	$-0.730691\pi$
$263$	−21.5021			−1.32588			−0.662938	+	0.748674i	$0.730691\pi$
$264$		0			0
$265$	−6.59549			−0.405158
$266$		0			0
$267$	8.04204	−	19.5240i	0.492165	−	1.19485i
$268$		0			0
$269$	−9.94281	−	13.6851i	−0.606224	−	0.834395i	0.390036	−	0.920799i	$-0.372462\pi$
$269$	−9.94281	−	13.6851i	−0.606224	−	0.834395i	−0.996260	+	0.0864040i	$0.972462\pi$
$270$		0			0
$271$	−23.7625	+	7.72091i	−1.44347	+	0.469012i	−0.922977	−	0.384854i	$-0.874252\pi$
$271$	−23.7625	+	7.72091i	−1.44347	+	0.469012i	−0.520493	+	0.853866i	$0.674252\pi$
$272$		0			0
$273$	−15.6493	+	18.3964i	−0.947141	+	1.11340i
$274$		0			0
$275$	−1.57805	−	3.24544i	−0.0951597	−	0.195707i
$276$		0			0
$277$	−2.78013	+	3.82652i	−0.167042	+	0.229913i	−0.884329	−	0.466865i	$-0.845384\pi$
$277$	−2.78013	+	3.82652i	−0.167042	+	0.229913i	0.717287	+	0.696778i	$0.245384\pi$
$278$		0			0
$279$	−2.42745	−	14.9445i	−0.145328	−	0.894702i
$280$		0			0
$281$	13.0447	−	9.47749i	0.778179	−	0.565380i	−0.126253	−	0.991998i	$-0.540295\pi$
$281$	13.0447	−	9.47749i	0.778179	−	0.565380i	0.904432	+	0.426618i	$0.140295\pi$
$282$		0			0
$283$	−22.9146	−	7.44542i	−1.36213	−	0.442584i	−0.465379	−	0.885112i	$-0.654082\pi$
$283$	−22.9146	−	7.44542i	−1.36213	−	0.442584i	−0.896755	+	0.442527i	$0.854082\pi$
$284$		0			0
$285$	−1.72974	+	22.5470i	−0.102461	+	1.33557i
$286$		0			0
$287$			40.3410i			2.38125i
$288$		0			0
$289$	−4.83765	+	14.8888i	−0.284568	+	0.875809i
$290$		0			0
$291$	−2.80368	−	4.55500i	−0.164355	−	0.267019i
$292$		0			0
$293$	−4.60821	−	14.1826i	−0.269215	−	0.828558i	−0.990692	−	0.136120i	$-0.956537\pi$
$293$	−4.60821	−	14.1826i	−0.269215	−	0.828558i	0.721478	−	0.692438i	$-0.243463\pi$
$294$		0			0
$295$	−24.6035	−	17.8755i	−1.43247	−	1.04075i
$296$		0			0
$297$	−15.8365	−	6.79744i	−0.918927	−	0.394427i
$298$		0			0
$299$	22.4053	+	16.2784i	1.29573	+	0.941404i
$300$		0			0
$301$	1.45335	+	4.47294i	0.0837695	+	0.257816i
$302$		0			0
$303$	3.28424	+	5.33573i	0.188674	+	0.306530i
$304$		0			0
$305$	6.06463	−	18.6650i	0.347260	−	1.06876i
$306$		0			0
$307$		−	7.86496i		−	0.448877i	−0.974488	−	0.224439i	$-0.927945\pi$
$307$		−	7.86496i		−	0.448877i	0.974488	−	0.224439i	$-0.0720548\pi$
$308$		0			0
$309$	−0.716431	+	9.33861i	−0.0407563	+	0.531255i
$310$		0			0
$311$	9.19784	+	2.98856i	0.521562	+	0.169466i	0.557954	−	0.829872i	$-0.311587\pi$
$311$	9.19784	+	2.98856i	0.521562	+	0.169466i	−0.0363921	+	0.999338i	$0.511587\pi$
$312$		0			0
$313$	−7.32629	+	5.32286i	−0.414106	+	0.300866i	−0.775262	−	0.631640i	$-0.782382\pi$
$313$	−7.32629	+	5.32286i	−0.414106	+	0.300866i	0.361156	+	0.932505i	$0.382382\pi$
$314$		0			0
$315$	−4.25075	−	26.1695i	−0.239503	−	1.47449i
$316$		0			0
$317$	2.48353	−	3.41829i	0.139489	−	0.191990i	−0.733557	−	0.679628i	$-0.762141\pi$
$317$	2.48353	−	3.41829i	0.139489	−	0.191990i	0.873046	+	0.487638i	$0.162141\pi$
$318$		0			0
$319$	−7.34393	−	3.91625i	−0.411181	−	0.219268i
$320$		0			0
$321$	11.0315	−	12.9679i	0.615717	−	0.723798i
$322$		0			0
$323$	5.83627	−	1.89632i	0.324739	−	0.105514i
$324$		0			0
$325$	−2.48992	−	3.42709i	−0.138116	−	0.190101i
$326$		0			0
$327$	11.3681	−	27.5988i	0.628655	−	1.52622i
$328$		0			0
$329$	21.3664			1.17797
$330$		0			0
$331$	24.5669			1.35032			0.675159	−	0.737672i	$-0.264075\pi$
$331$	24.5669			1.35032			0.675159	+	0.737672i	$0.264075\pi$
$332$		0			0
$333$	0.540340	−	1.07090i	0.0296104	−	0.0586850i
$334$		0			0
$335$	5.62043	+	7.73586i	0.307077	+	0.422655i
$336$		0			0
$337$	4.71231	−	1.53112i	0.256696	−	0.0834056i	−0.177842	−	0.984059i	$-0.556912\pi$
$337$	4.71231	−	1.53112i	0.256696	−	0.0834056i	0.434538	+	0.900653i	$0.356912\pi$
$338$		0			0
$339$	16.4282	+	13.9751i	0.892259	+	0.759022i
$340$		0			0
$341$	16.5782	−	2.30945i	0.897758	−	0.125064i
$342$		0			0
$343$	−2.46617	+	3.39439i	−0.133160	+	0.183280i
$344$		0			0
$345$	−29.5469	+	7.15526i	−1.59075	+	0.385226i
$346$		0			0
$347$	−1.56203	+	1.13488i	−0.0838542	+	0.0609237i	−0.628922	−	0.777468i	$-0.716504\pi$
$347$	−1.56203	+	1.13488i	−0.0838542	+	0.0609237i	0.545068	+	0.838392i	$0.316504\pi$
$348$		0			0
$349$	12.5123	+	4.06551i	0.669771	+	0.217622i	0.624111	−	0.781335i	$-0.285461\pi$
$349$	12.5123	+	4.06551i	0.669771	+	0.217622i	0.0456592	+	0.998957i	$0.485461\pi$
$350$		0			0
$351$	−19.6983	−	4.60602i	−1.05142	−	0.245851i
$352$		0			0
$353$			19.4850i			1.03708i	0.855052	+	0.518542i	$0.173525\pi$
$353$			19.4850i			1.03708i	−0.855052	+	0.518542i	$0.826475\pi$
$354$		0			0
$355$	−2.45596	+	7.55867i	−0.130349	+	0.401172i
$356$		0			0
$357$	−6.12713	+	3.77135i	−0.324282	+	0.199601i
$358$		0			0
$359$	3.52666	+	10.8539i	0.186130	+	0.572849i	0.999966	−	0.00824573i	$-0.00262473\pi$
$359$	3.52666	+	10.8539i	0.186130	+	0.572849i	−0.813836	+	0.581094i	$0.802625\pi$
$360$		0			0
$361$	7.27938	+	5.28878i	0.383125	+	0.278357i
$362$		0			0
$363$	7.90874	−	17.3335i	0.415101	−	0.909775i
$364$		0			0
$365$	10.4654	+	7.60356i	0.547784	+	0.397989i
$366$		0			0
$367$	7.47211	+	22.9968i	0.390041	+	1.20042i	0.932757	+	0.360506i	$0.117396\pi$
$367$	7.47211	+	22.9968i	0.390041	+	1.20042i	−0.542716	+	0.839916i	$0.682604\pi$
$368$		0			0
$369$	−30.0457	+	15.4587i	−1.56412	+	0.804746i
$370$		0			0
$371$	2.95855	−	9.10548i	0.153600	−	0.472733i
$372$		0			0
$373$		−	29.4637i		−	1.52557i	−0.646650	−	0.762787i	$-0.723830\pi$
$373$		−	29.4637i		−	1.52557i	0.646650	−	0.762787i	$-0.276170\pi$
$374$		0			0
$375$	−16.6693	−	1.27882i	−0.860797	−	0.0660379i
$376$		0			0
$377$	−9.29160	−	3.01902i	−0.478542	−	0.155488i
$378$		0			0
$379$	13.7061	−	9.95804i	0.704033	−	0.511510i	−0.177210	−	0.984173i	$-0.556707\pi$
$379$	13.7061	−	9.95804i	0.704033	−	0.511510i	0.881243	+	0.472663i	$0.156707\pi$
$380$		0			0
$381$	1.86843	+	7.71550i	0.0957227	+	0.395277i
$382$		0			0
$383$	−2.43171	+	3.34696i	−0.124254	+	0.171021i	−0.866612	−	0.498982i	$-0.833707\pi$
$383$	−2.43171	+	3.34696i	−0.124254	+	0.171021i	0.742358	+	0.670003i	$0.233707\pi$
$384$		0			0
$385$	29.0303	−	4.04412i	1.47952	−	0.206107i
$386$		0			0
$387$	−2.77449	+	2.79647i	−0.141035	+	0.142153i
$388$		0			0
$389$	0.812483	−	0.263992i	0.0411945	−	0.0133849i	−0.288347	−	0.957526i	$-0.593106\pi$
$389$	0.812483	−	0.263992i	0.0411945	−	0.0133849i	0.329542	+	0.944141i	$0.393106\pi$
$390$		0			0
$391$	4.84923	+	6.67439i	0.245236	+	0.337538i
$392$		0			0
$393$	15.6591	+	6.45006i	0.789899	+	0.325363i
$394$		0			0
$395$	−36.2286			−1.82286
$396$		0			0
$397$	−6.51344			−0.326900			−0.163450	−	0.986552i	$-0.552262\pi$
$397$	−6.51344			−0.326900			−0.163450	+	0.986552i	$0.552262\pi$
$398$		0			0
$399$	−30.3516	−	12.5019i	−1.51948	−	0.625880i
$400$		0			0
$401$	2.76297	+	3.80290i	0.137976	+	0.189908i	0.872413	−	0.488769i	$-0.162554\pi$
$401$	2.76297	+	3.80290i	0.137976	+	0.189908i	−0.734437	+	0.678676i	$0.762554\pi$
$402$		0			0
$403$	18.6865	−	6.07160i	0.930839	−	0.302448i
$404$		0			0
$405$	17.8620	−	13.1941i	0.887569	−	0.655619i
$406$		0			0
$407$	1.17012	+	0.623981i	0.0580006	+	0.0309296i
$408$		0			0
$409$	−0.453254	+	0.623851i	−0.0224120	+	0.0308474i	−0.820076	−	0.572255i	$-0.806069\pi$
$409$	−0.453254	+	0.623851i	−0.0224120	+	0.0308474i	0.797664	+	0.603102i	$0.206069\pi$
$410$		0			0
$411$	4.04143	+	16.6887i	0.199349	+	0.823191i
$412$		0			0
$413$	35.7146	−	25.9482i	1.75740	−	1.27683i
$414$		0			0
$415$	8.48868	+	2.75814i	0.416693	+	0.135392i
$416$		0			0
$417$	18.2828	+	1.40260i	0.895310	+	0.0686856i
$418$		0			0
$419$		−	11.7786i		−	0.575422i	−0.957717	−	0.287711i	$-0.907106\pi$
$419$		−	11.7786i		−	0.575422i	0.957717	−	0.287711i	$-0.0928943\pi$
$420$		0			0
$421$	4.31809	−	13.2897i	0.210451	−	0.647701i	−0.788994	−	0.614400i	$-0.789398\pi$
$421$	4.31809	−	13.2897i	0.210451	−	0.647701i	0.999445	−	0.0333010i	$-0.0106020\pi$
$422$		0			0
$423$	8.18761	+	15.9136i	0.398095	+	0.773744i
$424$		0			0
$425$	−0.389951	−	1.20015i	−0.0189154	−	0.0582157i
$426$		0			0
$427$	23.0478	+	16.7452i	1.11536	+	0.810356i
$428$		0			0
$429$	5.58317	−	21.6566i	0.269558	−	1.04559i
$430$		0			0
$431$	6.79130	+	4.93417i	0.327126	+	0.237671i	0.739210	−	0.673475i	$-0.235199\pi$
$431$	6.79130	+	4.93417i	0.327126	+	0.237671i	−0.412084	+	0.911146i	$0.635199\pi$
$432$		0			0
$433$	−0.0797922	−	0.245575i	−0.00383457	−	0.0118016i	0.949121	−	0.314912i	$-0.101975\pi$
$433$	−0.0797922	−	0.245575i	−0.00383457	−	0.0118016i	−0.952955	+	0.303110i	$0.901975\pi$
$434$		0			0
$435$	9.13309	−	5.62158i	0.437898	−	0.269534i
$436$		0			0
$437$	−11.6314	+	35.7977i	−0.556404	+	1.71244i
$438$		0			0
$439$			21.7453i			1.03785i	0.854821	+	0.518923i	$0.173667\pi$
$439$			21.7453i			1.03785i	−0.854821	+	0.518923i	$0.826333\pi$
$440$		0			0
$441$	17.2811	+	2.66721i	0.822910	+	0.127010i
$442$		0			0
$443$	−0.829709	−	0.269589i	−0.0394207	−	0.0128086i	0.289240	−	0.957257i	$-0.406597\pi$
$443$	−0.829709	−	0.269589i	−0.0394207	−	0.0128086i	−0.328661	+	0.944448i	$0.606597\pi$
$444$		0			0
$445$	−24.3354	+	17.6807i	−1.15361	+	0.838144i
$446$		0			0
$447$	−13.4420	+	3.25519i	−0.635784	+	0.153965i
$448$		0			0
$449$	8.71051	−	11.9890i	0.411074	−	0.565795i	−0.552406	−	0.833575i	$-0.686290\pi$
$449$	8.71051	−	11.9890i	0.411074	−	0.565795i	0.963480	+	0.267780i	$0.0862901\pi$
$450$		0			0
$451$	−16.3349	−	33.5946i	−0.769180	−	1.58191i
$452$		0			0
$453$	−11.1136	−	9.45402i	−0.522160	−	0.444189i
$454$		0			0
$455$	32.7222	−	10.6321i	1.53404	−	0.498440i
$456$		0			0
$457$	−20.3100	−	27.9544i	−0.950064	−	1.30765i	−0.951499	−	0.307652i	$-0.900457\pi$
$457$	−20.3100	−	27.9544i	−0.950064	−	1.30765i	0.00143531	−	0.999999i	$-0.499543\pi$
$458$		0			0
$459$	−5.15679	−	3.11826i	−0.240698	−	0.145548i
$460$		0			0
$461$	−23.7180			−1.10466			−0.552328	−	0.833627i	$-0.686260\pi$
$461$	−23.7180			−1.10466			−0.552328	+	0.833627i	$0.686260\pi$
$462$		0			0
$463$	−22.1878			−1.03116			−0.515578	−	0.856843i	$-0.672423\pi$
$463$	−22.1878			−1.03116			−0.515578	+	0.856843i	$0.672423\pi$
$464$		0			0
$465$	−8.21449	+	19.9427i	−0.380938	+	0.924821i
$466$		0			0
$467$	0.774712	+	1.06630i	0.0358494	+	0.0493424i	0.826565	−	0.562841i	$-0.190292\pi$
$467$	0.774712	+	1.06630i	0.0358494	+	0.0493424i	−0.790716	+	0.612183i	$0.790292\pi$
$468$		0			0
$469$	−13.2010	+	4.28926i	−0.609565	+	0.198060i
$470$		0			0
$471$	−15.9491	+	18.7487i	−0.734894	+	0.863895i
$472$		0			0
$473$	−3.02148	−	3.13643i	−0.138928	−	0.144213i
$474$		0			0
$475$	3.38409	−	4.65780i	0.155273	−	0.213714i
$476$		0			0
$477$	7.91541	−	1.28571i	0.362422	−	0.0588687i
$478$		0			0
$479$	3.61934	−	2.62960i	0.165372	−	0.120150i	−0.502021	−	0.864855i	$-0.667410\pi$
$479$	3.61934	−	2.62960i	0.165372	−	0.120150i	0.667393	+	0.744706i	$0.267410\pi$
$480$		0			0
$481$	1.48044	+	0.481025i	0.0675024	+	0.0219328i
$482$		0			0
$483$	3.37562	−	44.0009i	0.153596	−	2.00211i
$484$		0			0
$485$			7.61954i			0.345985i
$486$		0			0
$487$	−6.33410	+	19.4943i	−0.287025	+	0.883373i	0.698759	+	0.715357i	$0.253736\pi$
$487$	−6.33410	+	19.4943i	−0.287025	+	0.883373i	−0.985784	+	0.168016i	$0.946264\pi$
$488$		0			0
$489$	7.68991	+	12.4934i	0.347750	+	0.564972i
$490$		0			0
$491$	4.63109	+	14.2530i	0.208998	+	0.643231i	0.999525	+	0.0308038i	$0.00980670\pi$
$491$	4.63109	+	14.2530i	0.208998	+	0.643231i	−0.790527	+	0.612427i	$0.790193\pi$
$492$		0			0
$493$	−2.35452	−	1.71066i	−0.106042	−	0.0770442i
$494$		0			0
$495$	14.1365	+	20.0719i	0.635386	+	0.902164i
$496$		0			0
$497$	−9.33352	−	6.78120i	−0.418666	−	0.304178i
$498$		0			0
$499$	6.64060	+	20.4377i	0.297274	+	0.914916i	0.982448	+	0.186537i	$0.0597263\pi$
$499$	6.64060	+	20.4377i	0.297274	+	0.914916i	−0.685174	+	0.728380i	$0.740274\pi$
$500$		0			0
$501$	−15.4166	−	25.0466i	−0.688765	−	1.11900i
$502$		0			0
$503$	−5.10961	+	15.7258i	−0.227826	+	0.701177i	0.770166	+	0.637843i	$0.220173\pi$
$503$	−5.10961	+	15.7258i	−0.227826	+	0.701177i	−0.997992	+	0.0633335i	$0.979827\pi$
$504$		0			0
$505$		−	8.92553i		−	0.397181i
$506$		0			0
$507$	0.285778	−	3.72509i	0.0126918	−	0.165437i
$508$		0			0
$509$	−9.86951	−	3.20680i	−0.437459	−	0.142139i	0.0820042	−	0.996632i	$-0.473868\pi$
$509$	−9.86951	−	3.20680i	−0.437459	−	0.142139i	−0.519463	+	0.854493i	$0.673868\pi$
$510$		0			0
$511$	−15.1917	+	11.0374i	−0.672039	+	0.488265i
$512$		0			0
$513$	−2.31936	−	27.3964i	−0.102402	−	1.20958i
$514$		0			0
$515$	7.84251	−	10.7943i	0.345582	−	0.475653i
$516$		0			0
$517$	−17.7932	+	8.65170i	−0.782546	+	0.380501i
$518$		0			0
$519$	−9.17187	+	10.7819i	−0.402600	+	0.473272i
$520$		0			0
$521$	−8.01021	+	2.60268i	−0.350934	+	0.114025i	−0.479179	−	0.877717i	$-0.659066\pi$
$521$	−8.01021	+	2.60268i	−0.350934	+	0.114025i	0.128245	+	0.991742i	$0.459066\pi$
$522$		0			0
$523$	7.81238	+	10.7528i	0.341612	+	0.470188i	0.944911	−	0.327327i	$-0.106148\pi$
$523$	7.81238	+	10.7528i	0.341612	+	0.470188i	−0.603300	+	0.797515i	$0.706148\pi$
$524$		0			0
$525$	−2.57085	+	6.24137i	−0.112201	+	0.272396i
$526$		0			0
$527$	5.85304			0.254962
$528$		0			0
$529$	−27.6026			−1.20011
$530$		0			0
$531$	33.0118	+	16.6566i	1.43259	+	0.722837i
$532$		0			0
$533$	−25.7741	−	35.4749i	−1.11640	−	1.53659i
$534$		0			0
$535$	−23.0664	+	7.49473i	−0.997248	+	0.324026i
$536$		0			0
$537$	−27.0786	−	23.0351i	−1.16853	−	0.994036i
$538$		0			0
$539$	−3.37987	+	19.0334i	−0.145581	+	0.819828i
$540$		0			0
$541$	4.63993	−	6.38631i	0.199486	−	0.274569i	−0.697541	−	0.716545i	$-0.745722\pi$
$541$	4.63993	−	6.38631i	0.199486	−	0.274569i	0.897027	+	0.441976i	$0.145722\pi$
$542$		0			0
$543$	8.55509	−	2.07175i	0.367134	−	0.0889075i
$544$		0			0
$545$	−34.4000	+	24.9930i	−1.47353	+	1.07058i
$546$		0			0
$547$	12.8970	+	4.19049i	0.551436	+	0.179172i	0.571464	−	0.820627i	$-0.306376\pi$
$547$	12.8970	+	4.19049i	0.551436	+	0.179172i	−0.0200283	+	0.999799i	$0.506376\pi$
$548$		0			0
$549$	−3.63979	+	23.5826i	−0.155343	+	1.00648i
$550$		0			0
$551$		−	13.2782i		−	0.565671i
$552$		0			0
$553$	16.2511	−	50.0157i	0.691067	−	2.12689i
$554$		0			0
$555$	−1.45519	+	0.895693i	−0.0617693	+	0.0380201i
$556$		0			0
$557$	4.96236	+	15.2726i	0.210262	+	0.647119i	0.999456	+	0.0329757i	$0.0104984\pi$
$557$	4.96236	+	15.2726i	0.210262	+	0.647119i	−0.789194	+	0.614143i	$0.789502\pi$
$558$		0			0
$559$	−4.13582	−	3.00485i	−0.174927	−	0.127092i
$560$		0			0
$561$	3.57537	−	5.62166i	0.150952	−	0.237346i
$562$		0			0
$563$	−25.0393	−	18.1921i	−1.05528	−	0.766707i	−0.0820716	−	0.996626i	$-0.526154\pi$
$563$	−25.0393	−	18.1921i	−1.05528	−	0.766707i	−0.973210	+	0.229920i	$0.926154\pi$
$564$		0			0
$565$	−9.49460	−	29.2214i	−0.399441	−	1.22935i
$566$		0			0
$567$	10.2029	+	30.5780i	0.428480	+	1.28416i
$568$		0			0
$569$	11.2044	−	34.4836i	0.469713	−	1.44563i	−0.383245	−	0.923647i	$-0.625193\pi$
$569$	11.2044	−	34.4836i	0.469713	−	1.44563i	0.852957	−	0.521980i	$-0.174807\pi$
$570$		0			0
$571$			4.13275i			0.172950i	0.996254	+	0.0864752i	$0.0275603\pi$
$571$			4.13275i			0.172950i	−0.996254	+	0.0864752i	$0.972440\pi$
$572$		0			0
$573$	−0.806601	−	0.0618801i	−0.0336962	−	0.00258508i
$574$		0			0
$575$	7.36128	+	2.39183i	0.306987	+	0.0997460i
$576$		0			0
$577$	8.40294	−	6.10509i	0.349819	−	0.254158i	−0.398974	−	0.916962i	$-0.630634\pi$
$577$	8.40294	−	6.10509i	0.349819	−	0.254158i	0.748793	+	0.662804i	$0.230634\pi$
$578$		0			0
$579$	9.38878	+	38.7700i	0.390184	+	1.61123i
$580$		0			0
$581$	−7.61556	+	10.4819i	−0.315946	+	0.434863i
$582$		0			0
$583$	1.22321	+	8.78071i	0.0506603	+	0.363660i
$584$		0			0
$585$	20.4578	+	20.2970i	0.845828	+	0.839180i
$586$		0			0
$587$	−21.9463	+	7.13078i	−0.905821	+	0.294319i	−0.724637	−	0.689130i	$-0.757993\pi$
$587$	−21.9463	+	7.13078i	−0.905821	+	0.294319i	−0.181183	+	0.983449i	$0.557993\pi$
$588$		0			0
$589$	15.6962	+	21.6040i	0.646751	+	0.890176i
$590$		0			0
$591$	−25.3844	−	10.4559i	−1.04418	−	0.430100i
$592$		0			0
$593$	35.0442			1.43909			0.719546	−	0.694445i	$-0.244350\pi$
$593$	35.0442			1.43909			0.719546	+	0.694445i	$0.244350\pi$
$594$		0			0
$595$	10.2494			0.420183
$596$		0			0
$597$	19.7758	+	8.14574i	0.809370	+	0.333383i
$598$		0			0
$599$	−9.40748	−	12.9483i	−0.384379	−	0.529053i	0.572359	−	0.820003i	$-0.306028\pi$
$599$	−9.40748	−	12.9483i	−0.384379	−	0.529053i	−0.956738	+	0.290951i	$0.906028\pi$
$600$		0			0
$601$	−1.24254	+	0.403725i	−0.0506841	+	0.0164683i	−0.334249	−	0.942485i	$-0.608483\pi$
$601$	−1.24254	+	0.403725i	−0.0506841	+	0.0164683i	0.283565	+	0.958953i	$0.408483\pi$
$602$		0			0
$603$	−8.25323	−	8.18836i	−0.336098	−	0.333456i
$604$		0			0
$605$	−22.5379	+	15.1228i	−0.916298	+	0.614829i
$606$		0			0
$607$	19.2742	−	26.5287i	0.782318	−	1.07677i	−0.212705	−	0.977117i	$-0.568227\pi$
$607$	19.2742	−	26.5287i	0.782318	−	1.07677i	0.995022	−	0.0996514i	$-0.0317727\pi$
$608$		0			0
$609$	3.66409	+	15.1305i	0.148476	+	0.613117i
$610$		0			0
$611$	−18.7891	+	13.6511i	−0.760127	+	0.552265i
$612$		0			0
$613$	25.6908	+	8.34745i	1.03764	+	0.337150i	0.777807	−	0.628503i	$-0.216332\pi$
$613$	25.6908	+	8.34745i	1.03764	+	0.337150i	0.259835	+	0.965653i	$0.416332\pi$
$614$		0			0
$615$	47.9937	+	3.68193i	1.93529	+	0.148470i
$616$		0			0
$617$		−	39.1068i		−	1.57438i	−0.616711	−	0.787190i	$-0.711535\pi$
$617$		−	39.1068i		−	1.57438i	0.616711	−	0.787190i	$-0.288465\pi$
$618$		0			0
$619$	−5.63561	+	17.3446i	−0.226514	+	0.697139i	0.771620	+	0.636083i	$0.219447\pi$
$619$	−5.63561	+	17.3446i	−0.226514	+	0.697139i	−0.998134	+	0.0610553i	$0.980553\pi$
$620$		0			0
$621$	34.0651	−	14.3470i	1.36699	−	0.575726i
$622$		0			0
$623$	−13.4931	−	41.5275i	−0.540589	−	1.66376i
$624$		0			0
$625$	23.6690	+	17.1965i	0.946760	+	0.687861i
$626$		0			0
$627$	30.3381	−	1.87877i	1.21159	−	0.0750308i
$628$		0			0
$629$	0.375149	+	0.272561i	0.0149582	+	0.0108677i
$630$		0			0
$631$	−4.06842	−	12.5213i	−0.161961	−	0.498466i	0.836838	−	0.547450i	$-0.184402\pi$
$631$	−4.06842	−	12.5213i	−0.161961	−	0.498466i	−0.998800	+	0.0489844i	$0.984402\pi$
$632$		0			0
$633$	5.81420	−	3.57874i	0.231094	−	0.142242i
$634$		0			0
$635$	3.49463	−	10.7554i	0.138680	−	0.426813i
$636$		0			0
$637$			22.6918i			0.899082i
$638$		0			0
$639$	1.47399	−	9.55010i	0.0583100	−	0.377796i
$640$		0			0
$641$	14.8644	+	4.82975i	0.587110	+	0.190764i	0.587483	−	0.809236i	$-0.300119\pi$
$641$	14.8644	+	4.82975i	0.587110	+	0.190764i	−0.000372988		1.00000i	$0.500119\pi$
$642$		0			0
$643$	31.3232	−	22.7576i	1.23527	−	0.897473i	0.237992	−	0.971267i	$-0.423511\pi$
$643$	31.3232	−	22.7576i	1.23527	−	0.897473i	0.997273	+	0.0737942i	$0.0235108\pi$
$644$		0			0
$645$	5.45410	−	1.32080i	0.214755	−	0.0520064i
$646$		0			0
$647$	−10.1349	+	13.9495i	−0.398444	+	0.548411i	−0.960353	−	0.278788i	$-0.910067\pi$
$647$	−10.1349	+	13.9495i	−0.398444	+	0.548411i	0.561909	+	0.827199i	$0.310067\pi$
$648$		0			0
$649$	−19.2350	+	36.0703i	−0.755039	+	1.41588i
$650$		0			0
$651$	−23.8473	−	20.2863i	−0.934650	−	0.795083i
$652$		0			0
$653$	9.51038	−	3.09011i	0.372170	−	0.120925i	−0.116959	−	0.993137i	$-0.537315\pi$
$653$	9.51038	−	3.09011i	0.372170	−	0.120925i	0.489129	+	0.872211i	$0.337315\pi$
$654$		0			0
$655$	−14.1807	−	19.5180i	−0.554084	−	0.762632i
$656$		0			0
$657$	−14.0420	−	7.08512i	−0.547831	−	0.276417i
$658$		0			0
$659$	28.8109			1.12231			0.561157	−	0.827710i	$-0.310357\pi$
$659$	28.8109			1.12231			0.561157	+	0.827710i	$0.310357\pi$
$660$		0			0
$661$	45.7955			1.78124			0.890620	−	0.454748i	$-0.150271\pi$
$661$	45.7955			1.78124			0.890620	+	0.454748i	$0.150271\pi$
$662$		0			0
$663$	2.97852	−	7.23109i	0.115676	−	0.280832i
$664$		0			0
$665$	27.4859	+	37.8311i	1.06586	+	1.46703i
$666$		0			0
$667$	16.9774	−	5.51628i	0.657366	−	0.213591i
$668$		0			0
$669$	0.128838	−	0.151454i	0.00498118	−	0.00585556i
$670$		0			0
$671$	−25.9739	−	4.61232i	−1.00271	−	0.178057i
$672$		0			0
$673$	−13.2517	+	18.2394i	−0.510817	+	0.703079i	−0.984057	−	0.177854i	$-0.943084\pi$
$673$	−13.2517	+	18.2394i	−0.510817	+	0.703079i	0.473240	+	0.880934i	$0.343084\pi$
$674$		0			0
$675$	−5.63368	+	0.476943i	−0.216840	+	0.0183576i
$676$		0			0
$677$	−4.23918	+	3.07995i	−0.162925	+	0.118372i	−0.666260	−	0.745719i	$-0.732106\pi$
$677$	−4.23918	+	3.07995i	−0.162925	+	0.118372i	0.503335	+	0.864091i	$0.332106\pi$
$678$		0			0
$679$	−10.5192	−	3.41791i	−0.403691	−	0.131167i
$680$		0			0
$681$	−0.849505	+	11.0732i	−0.0325531	+	0.424327i
$682$		0			0
$683$		−	13.6438i		−	0.522067i	−0.965330	−	0.261034i	$-0.915937\pi$
$683$		−	13.6438i		−	0.522067i	0.965330	−	0.261034i	$-0.0840633\pi$
$684$		0			0
$685$	7.55889	−	23.2639i	0.288810	−	0.888867i
$686$		0			0
$687$	−17.1420	−	27.8497i	−0.654008	−	1.06253i
$688$		0			0
$689$	3.21585	+	9.89738i	0.122514	+	0.377060i
$690$		0			0
$691$	−15.7684	−	11.4564i	−0.599858	−	0.435822i	0.245971	−	0.969277i	$-0.420893\pi$
$691$	−15.7684	−	11.4564i	−0.599858	−	0.435822i	−0.845828	+	0.533455i	$0.820893\pi$
$692$		0			0
$693$	−34.0517	+	10.5126i	−1.29352	+	0.399339i
$694$		0			0
$695$	−21.1326	−	15.3537i	−0.801605	−	0.582400i
$696$		0			0
$697$	−4.03652	−	12.4231i	−0.152894	−	0.470560i
$698$		0			0
$699$	18.2328	+	29.6219i	0.689629	+	1.12040i
$700$		0			0
$701$	−11.2791	+	34.7135i	−0.426006	+	1.31111i	0.476022	+	0.879433i	$0.342078\pi$
$701$	−11.2791	+	34.7135i	−0.426006	+	1.31111i	−0.902028	+	0.431678i	$0.857922\pi$
$702$		0			0
$703$			2.11563i			0.0797926i
$704$		0			0
$705$	1.95012	−	25.4196i	0.0734457	−	0.957358i
$706$		0			0
$707$	12.3222	+	4.00373i	0.463425	+	0.150576i
$708$		0			0
$709$	−22.4559	+	16.3152i	−0.843351	+	0.612730i	−0.923305	−	0.384068i	$-0.874523\pi$
$709$	−22.4559	+	16.3152i	−0.843351	+	0.612730i	0.0799540	+	0.996799i	$0.474523\pi$
$710$		0			0
$711$	43.4788	−	7.06232i	1.63058	−	0.264858i
$712$		0			0
$713$	−21.1018	+	29.0441i	−0.790268	+	1.08771i
$714$		0			0
$715$	−22.9448	+	22.1039i	−0.858087	+	0.826640i
$716$		0			0
$717$	18.1898	−	21.3828i	0.679310	−	0.798554i
$718$		0			0
$719$	−7.12008	+	2.31345i	−0.265534	+	0.0862773i	−0.438758	−	0.898605i	$-0.644582\pi$
$719$	−7.12008	+	2.31345i	−0.265534	+	0.0862773i	0.173224	+	0.984882i	$0.444582\pi$
$720$		0			0
$721$	11.3842	+	15.6691i	0.423971	+	0.583546i
$722$		0			0
$723$	−12.0053	+	29.1459i	−0.446482	+	1.08395i
$724$		0			0
$725$	−2.73047			−0.101407
$726$		0			0
$727$	22.9120			0.849758			0.424879	−	0.905250i	$-0.360317\pi$
$727$	22.9120			0.849758			0.424879	+	0.905250i	$0.360317\pi$
$728$		0			0
$729$	−18.8646	+	19.3165i	−0.698688	+	0.715427i
$730$		0			0
$731$	−0.895125	−	1.23203i	−0.0331074	−	0.0455684i
$732$		0			0
$733$	−18.4596	+	5.99790i	−0.681822	+	0.221537i	−0.629393	−	0.777087i	$-0.716696\pi$
$733$	−18.4596	+	5.99790i	−0.681822	+	0.221537i	−0.0524291	+	0.998625i	$0.516696\pi$
$734$		0			0
$735$	−18.9731	−	16.1400i	−0.699834	−	0.595331i
$736$		0			0
$737$	9.25654	−	8.91731i	0.340969	−	0.328473i
$738$		0			0
$739$	−17.6574	+	24.3034i	−0.649540	+	0.894014i	−0.999079	−	0.0429071i	$-0.986338\pi$
$739$	−17.6574	+	24.3034i	−0.649540	+	0.894014i	0.349540	+	0.936922i	$0.386338\pi$
$740$		0			0
$741$	34.6780	−	8.39784i	1.27393	−	0.308502i
$742$		0			0
$743$	21.2863	−	15.4654i	0.780917	−	0.567369i	−0.124337	−	0.992240i	$-0.539680\pi$
$743$	21.2863	−	15.4654i	0.780917	−	0.567369i	0.905254	+	0.424871i	$0.139680\pi$
$744$		0			0
$745$	18.7380	+	6.08836i	0.686509	+	0.223060i
$746$		0			0
$747$	−10.7251	−	1.65534i	−0.392412	−	0.0605659i
$748$		0			0
$749$		−	35.2065i		−	1.28642i
$750$		0			0
$751$	1.03232	−	3.17716i	0.0376699	−	0.115936i	−0.930453	−	0.366411i	$-0.880587\pi$
$751$	1.03232	−	3.17716i	0.0376699	−	0.115936i	0.968123	+	0.250474i	$0.0805866\pi$
$752$		0			0
$753$	−4.07288	+	2.50693i	−0.148424	+	0.0913575i
$754$		0			0
$755$	6.42302	+	19.7680i	0.233758	+	0.719432i
$756$		0			0
$757$	8.85889	+	6.43636i	0.321982	+	0.233933i	0.737021	−	0.675870i	$-0.236232\pi$
$757$	8.85889	+	6.43636i	0.321982	+	0.233933i	−0.415039	+	0.909804i	$0.636232\pi$
$758$		0			0
$759$	15.0058	+	38.0094i	0.544675	+	1.37965i
$760$		0			0
$761$	−42.2752	−	30.7148i	−1.53248	−	1.11341i	−0.954842	−	0.297114i	$-0.903976\pi$
$761$	−42.2752	−	30.7148i	−1.53248	−	1.11341i	−0.577634	−	0.816296i	$-0.696024\pi$
$762$		0			0
$763$	−19.0736	−	58.7024i	−0.690509	−	2.12517i
$764$		0			0
$765$	3.92755	+	7.63365i	0.142001	+	0.275995i
$766$		0			0
$767$	−14.8282	+	45.6364i	−0.535414	+	1.64784i
$768$		0			0
$769$		−	27.2199i		−	0.981576i	−0.871279	−	0.490788i	$-0.836709\pi$
$769$		−	27.2199i		−	0.981576i	0.871279	−	0.490788i	$-0.163291\pi$
$770$		0			0
$771$	−43.8436	−	3.36355i	−1.57899	−	0.121135i
$772$		0			0
$773$	47.2966	+	15.3676i	1.70114	+	0.552734i	0.988819	−	0.149119i	$-0.0476437\pi$
$773$	47.2966	+	15.3676i	1.70114	+	0.552734i	0.712322	+	0.701853i	$0.247644\pi$
$774$		0			0
$775$	4.44255	−	3.22770i	0.159581	−	0.115942i
$776$		0			0
$777$	−0.583804	−	2.41076i	−0.0209438	−	0.0864854i
$778$		0			0
$779$	35.0298	−	48.2144i	1.25507	−	1.72746i
$780$		0			0
$781$	10.5185	+	1.86782i	0.376381	+	0.0668360i
$782$		0			0
$783$	−9.86498	+	8.52698i	−0.352546	+	0.304729i
$784$		0			0
$785$	33.3489	−	10.8357i	1.19027	−	0.386743i
$786$		0			0
$787$	−29.3174	−	40.3519i	−1.04505	−	1.43839i	−0.893021	−	0.450016i	$-0.851418\pi$
$787$	−29.3174	−	40.3519i	−1.04505	−	1.43839i	−0.152032	−	0.988376i	$-0.548582\pi$
$788$		0			0
$789$	−34.4358	−	14.1843i	−1.22595	−	0.504973i
$790$		0			0
$791$	44.6009			1.58582
$792$		0			0
$793$	−30.9663			−1.09964
$794$		0			0
$795$	−10.5628	−	4.35084i	−0.374622	−	0.154309i
$796$		0			0
$797$	−4.27271	−	5.88088i	−0.151347	−	0.208311i	0.726611	−	0.687049i	$-0.241094\pi$
$797$	−4.27271	−	5.88088i	−0.151347	−	0.208311i	−0.877958	+	0.478738i	$0.841094\pi$
$798$		0			0
$799$	−6.57985	+	2.13792i	−0.232778	+	0.0756343i
$800$		0			0
$801$	25.7588	−	25.9629i	0.910143	−	0.917354i
$802$		0			0
$803$	8.18184	−	15.3430i	0.288731	−	0.541442i
$804$		0			0
$805$	−36.9517	+	50.8597i	−1.30238	+	1.79257i
$806$		0			0
$807$	−6.89588	−	28.4758i	−0.242746	−	1.00240i
$808$		0			0
$809$	−42.3362	+	30.7591i	−1.48846	+	1.08143i	−0.513757	+	0.857936i	$0.671747\pi$
$809$	−42.3362	+	30.7591i	−1.48846	+	1.08143i	−0.974705	+	0.223495i	$0.928253\pi$
$810$		0			0
$811$	−21.4029	−	6.95422i	−0.751557	−	0.244196i	−0.0919057	−	0.995768i	$-0.529296\pi$
$811$	−21.4029	−	6.95422i	−0.751557	−	0.244196i	−0.659651	+	0.751572i	$0.729296\pi$
$812$		0			0
$813$	−43.1492	−	3.31028i	−1.51331	−	0.116097i
$814$		0			0
$815$		−	20.8988i		−	0.732052i
$816$		0			0
$817$	2.14705	−	6.60794i	0.0751157	−	0.231182i
$818$		0			0
$819$	−37.1981	+	19.1386i	−1.29981	+	0.668757i
$820$		0			0
$821$	9.74448	+	29.9904i	0.340085	+	1.04667i	0.964163	+	0.265311i	$0.0854747\pi$
$821$	9.74448	+	29.9904i	0.340085	+	1.04667i	−0.624078	+	0.781362i	$0.714525\pi$
$822$		0			0
$823$	24.6626	+	17.9184i	0.859683	+	0.624596i	0.927799	−	0.373081i	$-0.121699\pi$
$823$	24.6626	+	17.9184i	0.859683	+	0.624596i	−0.0681155	+	0.997677i	$0.521699\pi$
$824$		0			0
$825$	−0.386342	−	6.23859i	−0.0134507	−	0.217200i
$826$		0			0
$827$	26.5754	+	19.3082i	0.924118	+	0.671411i	0.944546	−	0.328380i	$-0.106503\pi$
$827$	26.5754	+	19.3082i	0.924118	+	0.671411i	−0.0204274	+	0.999791i	$0.506503\pi$
$828$		0			0
$829$	11.1158	+	34.2108i	0.386066	+	1.18819i	0.935704	+	0.352786i	$0.114766\pi$
$829$	11.1158	+	34.2108i	0.386066	+	1.18819i	−0.549638	+	0.835403i	$0.685234\pi$
$830$		0			0
$831$	−6.97664	+	4.29424i	−0.242017	+	0.148966i
$832$		0			0
$833$	−2.08887	+	6.42889i	−0.0723752	+	0.222748i
$834$		0			0
$835$			41.8976i			1.44993i
$836$		0			0
$837$	5.97081	−	25.5350i	0.206382	−	0.882620i
$838$		0			0
$839$	−18.1168	−	5.88650i	−0.625460	−	0.203224i	−0.0208973	−	0.999782i	$-0.506652\pi$
$839$	−18.1168	−	5.88650i	−0.625460	−	0.203224i	−0.604563	+	0.796557i	$0.706652\pi$
$840$		0			0
$841$	18.3669	−	13.3443i	0.633340	−	0.460149i
$842$		0			0
$843$	27.1432	−	6.57316i	0.934860	−	0.226391i
$844$		0			0
$845$	−3.12831	+	4.30574i	−0.107617	+	0.148122i
$846$		0			0
$847$	−10.7680	−	37.8986i	−0.369994	−	1.30221i
$848$		0			0
$849$	−31.7865	−	27.0400i	−1.09091	−	0.928010i
$850$		0			0
$851$	−2.70503	+	0.878916i	−0.0927271	+	0.0301288i
$852$		0			0
$853$	−23.9395	−	32.9499i	−0.819672	−	1.12818i	−0.989758	−	0.142753i	$-0.954405\pi$
$853$	−23.9395	−	32.9499i	−0.819672	−	1.12818i	0.170086	−	0.985429i	$-0.445595\pi$
$854$		0			0
$855$	−17.6437	+	34.9682i	−0.603403	+	1.19589i
$856$		0			0
$857$	26.3250			0.899245			0.449622	−	0.893219i	$-0.351559\pi$
$857$	26.3250			0.899245			0.449622	+	0.893219i	$0.351559\pi$
$858$		0			0
$859$	24.9252			0.850436			0.425218	−	0.905091i	$-0.360197\pi$
$859$	24.9252			0.850436			0.425218	+	0.905091i	$0.360197\pi$
$860$		0			0
$861$	−26.6117	+	64.6065i	−0.906925	+	2.20179i
$862$		0			0
$863$	23.4553	+	32.2834i	0.798427	+	1.09894i	0.993007	+	0.118054i	$0.0376657\pi$
$863$	23.4553	+	32.2834i	0.798427	+	1.09894i	−0.194580	+	0.980887i	$0.562334\pi$
$864$		0			0
$865$	19.1780	−	6.23132i	0.652073	−	0.211871i
$866$		0			0
$867$	−17.5692	+	20.6533i	−0.596681	+	0.701421i
$868$		0			0
$869$	6.71902	+	48.2318i	0.227927	+	1.63615i
$870$		0			0
$871$	8.86822	−	12.2061i	0.300488	−	0.413586i
$872$		0			0
$873$	−1.48534	−	9.14439i	−0.0502710	−	0.309491i
$874$		0			0
$875$	−27.9690	+	20.3207i	−0.945525	+	0.686964i
$876$		0			0
$877$	−21.9967	−	7.14717i	−0.742776	−	0.241343i	−0.0869063	−	0.996216i	$-0.527698\pi$
$877$	−21.9967	−	7.14717i	−0.742776	−	0.241343i	−0.655870	+	0.754874i	$0.727698\pi$
$878$		0			0
$879$	1.97573	−	25.7535i	0.0666399	−	0.868645i
$880$		0			0
$881$			18.7662i			0.632249i	0.948718	+	0.316124i	$0.102382\pi$
$881$			18.7662i			0.632249i	−0.948718	+	0.316124i	$0.897618\pi$
$882$		0			0
$883$	13.9546	−	42.9478i	0.469609	−	1.44531i	−0.383483	−	0.923548i	$-0.625275\pi$
$883$	13.9546	−	42.9478i	0.469609	−	1.44531i	0.853092	−	0.521761i	$-0.174725\pi$
$884$		0			0
$885$	−27.6108	−	44.8579i	−0.928128	−	1.50788i
$886$		0			0
$887$	−12.2860	−	37.8123i	−0.412522	−	1.26961i	−0.914449	−	0.404702i	$-0.867375\pi$
$887$	−12.2860	−	37.8123i	−0.412522	−	1.26961i	0.501927	−	0.864910i	$-0.332625\pi$
$888$		0			0
$889$	13.2808	+	9.64909i	0.445425	+	0.323620i
$890$		0			0
$891$	−20.8783	−	21.3330i	−0.699448	−	0.714683i
$892$		0			0
$893$	−25.5365	−	18.5534i	−0.854548	−	0.620865i
$894$		0			0
$895$	15.6499	+	48.1655i	0.523119	+	1.60999i
$896$		0			0
$897$	25.1440	+	40.8501i	0.839533	+	1.36395i
$898$		0			0
$899$	3.91358	−	12.0447i	0.130525	−	0.401715i
$900$		0			0
$901$			3.10009i			0.103279i
$902$		0			0
$903$	−0.623111	+	8.12219i	−0.0207358	+	0.270290i
$904$		0			0
$905$	−11.9258	−	3.87491i	−0.396425	−	0.128806i
$906$		0			0
$907$	−39.1405	+	28.4372i	−1.29964	+	0.944243i	−0.999952	−	0.00979529i	$-0.996882\pi$
$907$	−39.1405	+	28.4372i	−1.29964	+	0.944243i	−0.299686	+	0.954038i	$0.596882\pi$
$908$		0			0
$909$	1.73992	+	10.7117i	0.0577096	+	0.355286i
$910$		0			0
$911$	4.26247	−	5.86679i	0.141222	−	0.194375i	−0.732547	−	0.680716i	$-0.761669\pi$
$911$	4.26247	−	5.86679i	0.141222	−	0.194375i	0.873769	+	0.486341i	$0.161669\pi$
$912$		0			0
$913$	2.09764	−	11.8127i	0.0694218	−	0.390943i
$914$		0			0
$915$	22.0253	−	25.8916i	0.728135	−	0.855949i
$916$		0			0
$917$	33.3068	−	10.8220i	1.09989	−	0.357375i
$918$		0			0
$919$	−19.5709	−	26.9371i	−0.645585	−	0.888572i	0.353313	−	0.935505i	$-0.385055\pi$
$919$	−19.5709	−	26.9371i	−0.645585	−	0.888572i	−0.998898	+	0.0469333i	$0.985055\pi$
$920$		0			0
$921$	5.18827	−	12.5958i	0.170959	−	0.415046i
$922$		0			0
$923$	12.5402			0.412767
$924$		0			0
$925$	0.435050			0.0143044
$926$		0			0
$927$	−7.30777	+	14.4833i	−0.240019	+	0.475693i
$928$		0			0
$929$	28.3716	+	39.0502i	0.930842	+	1.28119i	0.959530	+	0.281606i	$0.0908670\pi$
$929$	28.3716	+	39.0502i	0.930842	+	1.28119i	−0.0286883	+	0.999588i	$0.509133\pi$
$930$		0			0
$931$	−29.3313	+	9.53030i	−0.961293	+	0.312343i
$932$		0			0
$933$	12.7590	+	10.8537i	0.417710	+	0.355336i
$934$		0			0
$935$	−8.53532	+	4.15017i	−0.279135	+	0.135725i
$936$		0			0
$937$	−23.0348	+	31.7047i	−0.752516	+	1.03575i	0.245284	+	0.969451i	$0.421119\pi$
$937$	−23.0348	+	31.7047i	−0.752516	+	1.03575i	−0.997800	+	0.0662978i	$0.978881\pi$
$938$		0			0
$939$	−15.2445	+	3.69169i	−0.497484	+	0.120474i
$940$		0			0
$941$	31.1422	−	22.6261i	1.01521	−	0.737590i	0.0499114	−	0.998754i	$-0.484106\pi$
$941$	31.1422	−	22.6261i	1.01521	−	0.737590i	0.965295	+	0.261163i	$0.0841061\pi$
$942$		0			0
$943$	76.1992	+	24.7586i	2.48139	+	0.806251i
$944$		0			0
$945$	10.4556	−	44.7149i	0.340121	−	1.45457i
$946$		0			0
$947$		−	38.1571i		−	1.23994i	−0.784626	−	0.619970i	$-0.787145\pi$
$947$		−	38.1571i		−	1.23994i	0.784626	−	0.619970i	$-0.212855\pi$
$948$		0			0
$949$	6.30736	−	19.4120i	0.204745	−	0.630142i
$950$		0			0
$951$	6.23234	−	3.83611i	0.202097	−	0.124395i
$952$		0			0
$953$	3.62424	+	11.1543i	0.117401	+	0.361322i	0.992440	−	0.122729i	$-0.0391647\pi$
$953$	3.62424	+	11.1543i	0.117401	+	0.361322i	−0.875039	+	0.484052i	$0.839165\pi$
$954$		0			0
$955$	0.932331	+	0.677378i	0.0301695	+	0.0219194i
$956$		0			0
$957$	−9.17796	−	11.1165i	−0.296681	−	0.359345i
$958$		0			0
$959$	28.7265	+	20.8710i	0.927627	+	0.673960i
$960$		0			0
$961$	−1.70888	−	5.25939i	−0.0551252	−	0.169658i
$962$		0			0
$963$	26.2216	−	13.4911i	0.844978	−	0.434745i
$964$		0			0
$965$	17.5603	−	54.0451i	0.565287	−	1.73977i
$966$		0			0
$967$		−	17.9596i		−	0.577543i	−0.957398	−	0.288771i	$-0.906753\pi$
$967$		−	17.9596i		−	0.577543i	0.957398	−	0.288771i	$-0.0932467\pi$
$968$		0			0
$969$	10.5978	+	0.813032i	0.340450	+	0.0261184i
$970$		0			0
$971$	31.7800	+	10.3259i	1.01987	+	0.331375i	0.770777	−	0.637105i	$-0.219868\pi$
$971$	31.7800	+	10.3259i	1.01987	+	0.331375i	0.249091	+	0.968480i	$0.419868\pi$
$972$		0			0
$973$	30.6762	−	22.2876i	0.983435	−	0.714507i
$974$		0			0
$975$	−1.72690	−	7.13104i	−0.0553050	−	0.228376i
$976$		0			0
$977$	−24.4286	+	33.6231i	−0.781541	+	1.07570i	0.213570	+	0.976928i	$0.431491\pi$
$977$	−24.4286	+	33.6231i	−0.781541	+	1.07570i	−0.995110	+	0.0987706i	$0.968509\pi$
$978$		0			0
$979$	28.0519	+	29.1191i	0.896543	+	0.930649i
$980$		0			0
$981$	36.4121	−	36.7006i	1.16255	−	1.17176i
$982$		0			0
$983$	−34.0812	+	11.0737i	−1.08702	+	0.353195i	−0.797095	−	0.603854i	$-0.793631\pi$
$983$	−34.0812	+	11.0737i	−1.08702	+	0.353195i	−0.289927	+	0.957049i	$0.593631\pi$
$984$		0			0
$985$	22.9877	+	31.6399i	0.732450	+	1.00813i
$986$		0			0
$987$	34.2185	+	14.0948i	1.08919	+	0.448641i
$988$		0			0
$989$	9.34080			0.297020
$990$		0			0
$991$	17.1209			0.543863			0.271931	−	0.962317i	$-0.412338\pi$
$991$	17.1209			0.543863			0.271931	+	0.962317i	$0.412338\pi$
$992$		0			0
$993$	39.3441	+	16.2060i	1.24855	+	0.514282i
$994$		0			0
$995$	−17.9087	−	24.6492i	−0.567743	−	0.781431i
$996$		0			0
$997$	7.93613	−	2.57860i	0.251340	−	0.0816652i	−0.180638	−	0.983550i	$-0.557816\pi$
$997$	7.93613	−	2.57860i	0.251340	−	0.0816652i	0.431977	+	0.901885i	$0.357816\pi$
$998$		0			0
$999$	1.57180	−	1.35861i	0.0497296	−	0.0429847i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	132.2.p.a.29.4	yes	16
3.2	odd	2	inner	132.2.p.a.29.1	✓	16
4.3	odd	2		528.2.bn.d.161.1		16
11.5	even	5		1452.2.b.e.725.7		16
11.6	odd	10		1452.2.b.e.725.8		16
11.8	odd	10	inner	132.2.p.a.41.1	yes	16
12.11	even	2		528.2.bn.d.161.4		16
33.5	odd	10		1452.2.b.e.725.5		16
33.8	even	10	inner	132.2.p.a.41.4	yes	16
33.17	even	10		1452.2.b.e.725.6		16
44.19	even	10		528.2.bn.d.305.4		16
132.107	odd	10		528.2.bn.d.305.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.p.a.29.1	✓	16	3.2	odd	2	inner
132.2.p.a.29.4	yes	16	1.1	even	1	trivial
132.2.p.a.41.1	yes	16	11.8	odd	10	inner
132.2.p.a.41.4	yes	16	33.8	even	10	inner
528.2.bn.d.161.1		16	4.3	odd	2
528.2.bn.d.161.4		16	12.11	even	2
528.2.bn.d.305.1		16	132.107	odd	10
528.2.bn.d.305.4		16	44.19	even	10
1452.2.b.e.725.5		16	33.5	odd	10
1452.2.b.e.725.6		16	33.17	even	10
1452.2.b.e.725.7		16	11.5	even	5
1452.2.b.e.725.8		16	11.6	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 132 = 2^{2} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	132.p (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.60151 + 0.659669i) q^{3} +(-1.45030 - 1.99617i) q^{5} +(3.40640 - 1.10681i) q^{7} +(2.12967 + 2.11293i) q^{9} +(-2.38857 + 2.30103i) q^{11} +(-2.28837 + 3.14966i) q^{13} +(-1.00586 - 4.15361i) q^{15} +(-0.938264 + 0.681689i) q^{17} +(-5.03232 - 1.63510i) q^{19} +(6.18551 + 0.474534i) q^{21} -7.11355i q^{23} +(-0.336235 + 1.03483i) q^{25} +(2.01686 + 4.78877i) q^{27} +(0.775461 + 2.38662i) q^{29} +(-4.08293 - 2.96642i) q^{31} +(-5.34324 + 2.10946i) q^{33} +(-7.14969 - 5.19455i) q^{35} +(-0.123555 - 0.380264i) q^{37} +(-5.74258 + 3.53466i) q^{39} +(-3.48049 + 10.7118i) q^{41} +1.31310i q^{43} +(1.12911 - 7.31559i) q^{45} +(5.67347 + 1.84342i) q^{47} +(4.71542 - 3.42595i) q^{49} +(-1.95233 + 0.472788i) q^{51} +(1.57118 - 2.16254i) q^{53} +(8.05740 + 1.43080i) q^{55} +(-6.98069 - 5.93830i) q^{57} +(11.7221 - 3.80874i) q^{59} +(4.67521 + 6.43487i) q^{61} +(9.59313 + 4.84036i) q^{63} +9.60609 q^{65} -3.87535 q^{67} +(4.69259 - 11.3924i) q^{69} +(-1.89329 - 2.60589i) q^{71} +(-4.98614 + 1.62010i) q^{73} +(-1.22113 + 1.43548i) q^{75} +(-5.58962 + 10.4819i) q^{77} +(8.63038 - 11.8787i) q^{79} +(0.0710170 + 8.99972i) q^{81} +(-2.92652 + 2.12624i) q^{83} +(2.72153 + 0.884280i) q^{85} +(-0.332473 + 4.33375i) q^{87} -12.1910i q^{89} +(-4.30902 + 13.2618i) q^{91} +(-4.58200 - 7.44414i) q^{93} +(4.03445 + 12.4168i) q^{95} +(-2.49831 - 1.81513i) q^{97} +(-9.94880 - 0.146440i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{3} + 5 q^{9} + 9 q^{15} - 30 q^{19} - 12 q^{25} + q^{27} - 10 q^{31} - 41 q^{33} - 24 q^{37} - 35 q^{39} + 2 q^{45} + 12 q^{49} - 15 q^{51} + 62 q^{55} + 35 q^{57} + 40 q^{61} + 55 q^{63} + 44 q^{67}+ \cdots - 101 q^{99}+O(q^{100}) \) 16 * q + q^3 + 5 * q^9 + 9 * q^15 - 30 * q^19 - 12 * q^25 + q^27 - 10 * q^31 - 41 * q^33 - 24 * q^37 - 35 * q^39 + 2 * q^45 + 12 * q^49 - 15 * q^51 + 62 * q^55 + 35 * q^57 + 40 * q^61 + 55 * q^63 + 44 * q^67 + 46 * q^69 + 10 * q^73 + 21 * q^75 + 20 * q^79 + 57 * q^81 - 60 * q^85 - 60 * q^91 + 7 * q^93 - 36 * q^97 - 101 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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