LMFDB - Embedded newform 184.2.i.b.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [184,2,Mod(9,184)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(184, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("184.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 184 = 2^{3} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	184.i (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.46924739719$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			121.2
Character	$\chi$	$=$	184.121
Dual form			184.2.i.b.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.817468 + 0.240030i) q^{3} +(2.57662 - 1.65589i) q^{5} +(-0.181823 + 1.26461i) q^{7} +(-1.91312 - 1.22949i) q^{9} +O(q^{10})$	\(q+(0.817468 + 0.240030i) q^{3} +(2.57662 - 1.65589i) q^{5} +(-0.181823 + 1.26461i) q^{7} +(-1.91312 - 1.22949i) q^{9} +(0.0891963 + 0.195313i) q^{11} +(0.133237 + 0.926681i) q^{13} +(2.50377 - 0.735173i) q^{15} +(1.65894 - 1.91452i) q^{17} +(2.99577 + 3.45730i) q^{19} +(-0.452179 + 0.990134i) q^{21} +(-3.67385 + 3.08267i) q^{23} +(1.81991 - 3.98505i) q^{25} +(-2.94258 - 3.39592i) q^{27} +(-1.37099 + 1.58221i) q^{29} +(-6.97977 + 2.04945i) q^{31} +(0.0260342 + 0.181072i) q^{33} +(1.62557 + 3.55950i) q^{35} +(-8.67535 - 5.57531i) q^{37} +(-0.113515 + 0.789513i) q^{39} +(4.48304 - 2.88108i) q^{41} +(-9.26657 - 2.72091i) q^{43} -6.96529 q^{45} +5.35449 q^{47} +(5.15027 + 1.51226i) q^{49} +(1.81567 - 1.16686i) q^{51} +(-2.04664 + 14.2347i) q^{53} +(0.553242 + 0.355547i) q^{55} +(1.61909 + 3.54531i) q^{57} +(-0.584927 - 4.06826i) q^{59} +(-6.83371 + 2.00656i) q^{61} +(1.90267 - 2.19580i) q^{63} +(1.87778 + 2.16708i) q^{65} +(1.66308 - 3.64163i) q^{67} +(-3.74319 + 1.63815i) q^{69} +(2.94055 - 6.43891i) q^{71} +(2.53968 + 2.93095i) q^{73} +(2.44425 - 2.82082i) q^{75} +(-0.263212 + 0.0772860i) q^{77} +(-1.92588 - 13.3948i) q^{79} +(1.24378 + 2.72350i) q^{81} +(8.81386 + 5.66433i) q^{83} +(1.10422 - 7.68000i) q^{85} +(-1.50052 + 0.964324i) q^{87} +(4.62819 + 1.35896i) q^{89} -1.19611 q^{91} -6.19767 q^{93} +(13.4439 + 3.94748i) q^{95} +(9.77480 - 6.28188i) q^{97} +(0.0694913 - 0.483322i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 2 q^{3} - 13 q^{7} + 21 q^{9}+O(q^{10}) $ 30 * q + 2 * q^3 - 13 * q^7 + 21 * q^9	$ 30 q + 2 q^{3} - 13 q^{7} + 21 q^{9} + 2 q^{11} - 2 q^{15} - 22 q^{17} + 3 q^{19} + 2 q^{21} + q^{23} + 13 q^{25} - 31 q^{27} + 7 q^{29} + 18 q^{31} - 8 q^{33} + 41 q^{35} - 62 q^{37} + 6 q^{39} - 15 q^{41} - 47 q^{43} + 8 q^{45} - 72 q^{47} - 16 q^{49} - 7 q^{51} - 43 q^{53} - 9 q^{55} - 42 q^{57} - 11 q^{59} + 57 q^{61} - 62 q^{63} + 14 q^{65} - 27 q^{67} - 22 q^{69} + 48 q^{71} - 12 q^{73} + 87 q^{75} - 3 q^{77} + 8 q^{79} + 123 q^{81} - 18 q^{83} + 54 q^{85} + 137 q^{87} - 23 q^{89} + 142 q^{91} - 110 q^{93} + 119 q^{95} + 47 q^{97} - 17 q^{99}+O(q^{100}) $ 30 * q + 2 * q^3 - 13 * q^7 + 21 * q^9 + 2 * q^11 - 2 * q^15 - 22 * q^17 + 3 * q^19 + 2 * q^21 + q^23 + 13 * q^25 - 31 * q^27 + 7 * q^29 + 18 * q^31 - 8 * q^33 + 41 * q^35 - 62 * q^37 + 6 * q^39 - 15 * q^41 - 47 * q^43 + 8 * q^45 - 72 * q^47 - 16 * q^49 - 7 * q^51 - 43 * q^53 - 9 * q^55 - 42 * q^57 - 11 * q^59 + 57 * q^61 - 62 * q^63 + 14 * q^65 - 27 * q^67 - 22 * q^69 + 48 * q^71 - 12 * q^73 + 87 * q^75 - 3 * q^77 + 8 * q^79 + 123 * q^81 - 18 * q^83 + 54 * q^85 + 137 * q^87 - 23 * q^89 + 142 * q^91 - 110 * q^93 + 119 * q^95 + 47 * q^97 - 17 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/184\mathbb{Z}\right)^\times$.

$n$	$47$	$93$	$97$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{11}\right)$

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
$3$	0.817468	+	0.240030i	0.471965	+	0.138582i	0.509061	−	0.860730i	$-0.329993\pi$
$3$	0.817468	+	0.240030i	0.471965	+	0.138582i	−0.0370961	+	0.999312i	$0.511811\pi$
$4$		0			0
$5$	2.57662	−	1.65589i	1.15230	−	0.740538i	0.182204	−	0.983261i	$-0.441677\pi$
$5$	2.57662	−	1.65589i	1.15230	−	0.740538i	0.970096	+	0.242723i	$0.0780406\pi$
$6$		0			0
$7$	−0.181823	+	1.26461i	−0.0687227	+	0.477977i	0.926175	+	0.377093i	$0.123076\pi$
$7$	−0.181823	+	1.26461i	−0.0687227	+	0.477977i	−0.994898	+	0.100884i	$0.967833\pi$
$8$		0			0
$9$	−1.91312	−	1.22949i	−0.637707	−	0.409829i
$10$		0			0
$11$	0.0891963	+	0.195313i	0.0268937	+	0.0588890i	0.922602	−	0.385753i	$-0.126058\pi$
$11$	0.0891963	+	0.195313i	0.0268937	+	0.0588890i	−0.895708	+	0.444642i	$0.853331\pi$
$12$		0			0
$13$	0.133237	+	0.926681i	0.0369532	+	0.257015i	0.999921	−	0.0126028i	$-0.00401171\pi$
$13$	0.133237	+	0.926681i	0.0369532	+	0.257015i	−0.962967	+	0.269618i	$0.913103\pi$
$14$		0			0
$15$	2.50377	−	0.735173i	0.646470	−	0.189821i
$16$		0			0
$17$	1.65894	−	1.91452i	0.402351	−	0.464338i	−0.518029	−	0.855363i	$-0.673334\pi$
$17$	1.65894	−	1.91452i	0.402351	−	0.464338i	0.920380	+	0.391025i	$0.127879\pi$
$18$		0			0
$19$	2.99577	+	3.45730i	0.687276	+	0.793159i	0.986975	−	0.160875i	$-0.0514316\pi$
$19$	2.99577	+	3.45730i	0.687276	+	0.793159i	−0.299699	+	0.954034i	$0.596886\pi$
$20$		0			0
$21$	−0.452179	+	0.990134i	−0.0986736	+	0.216065i
$22$		0			0
$23$	−3.67385	+	3.08267i	−0.766050	+	0.642781i
$23$	−3.67385	+	3.08267i	−0.766050	+	0.642781i
$24$		0			0
$25$	1.81991	−	3.98505i	0.363982	−	0.797010i
$26$		0			0
$27$	−2.94258	−	3.39592i	−0.566301	−	0.653546i
$28$		0			0
$29$	−1.37099	+	1.58221i	−0.254586	+	0.293808i	−0.868627	−	0.495466i	$-0.834997\pi$
$29$	−1.37099	+	1.58221i	−0.254586	+	0.293808i	0.614041	+	0.789274i	$0.289543\pi$
$30$		0			0
$31$	−6.97977	+	2.04945i	−1.25360	+	0.368091i	−0.840110	−	0.542416i	$-0.817510\pi$
$31$	−6.97977	+	2.04945i	−1.25360	+	0.368091i	−0.413493	+	0.910507i	$0.635692\pi$
$32$		0			0
$33$	0.0260342	+	0.181072i	0.00453197	+	0.0315205i
$34$		0			0
$35$	1.62557	+	3.55950i	0.274771	+	0.601665i
$36$		0			0
$37$	−8.67535	−	5.57531i	−1.42622	−	0.916575i	−0.999928	−	0.0119889i	$-0.996184\pi$
$37$	−8.67535	−	5.57531i	−1.42622	−	0.916575i	−0.426291	−	0.904586i	$-0.640180\pi$
$38$		0			0
$39$	−0.113515	+	0.789513i	−0.0181769	+	0.126423i
$40$		0			0
$41$	4.48304	−	2.88108i	0.700133	−	0.449948i	−0.141542	−	0.989932i	$-0.545206\pi$
$41$	4.48304	−	2.88108i	0.700133	−	0.449948i	0.841675	+	0.539984i	$0.181570\pi$
$42$		0			0
$43$	−9.26657	−	2.72091i	−1.41314	−	0.414935i	−0.515964	−	0.856610i	$-0.672566\pi$
$43$	−9.26657	−	2.72091i	−1.41314	−	0.414935i	−0.897175	+	0.441675i	$0.854384\pi$
$44$		0			0
$45$	−6.96529			−1.03832
$46$		0			0
$47$	5.35449			0.781033			0.390516	−	0.920596i	$-0.372297\pi$
$47$	5.35449			0.781033			0.390516	+	0.920596i	$0.372297\pi$
$48$		0			0
$49$	5.15027	+	1.51226i	0.735754	+	0.216037i
$50$		0			0
$51$	1.81567	−	1.16686i	0.254245	−	0.163393i
$52$		0			0
$53$	−2.04664	+	14.2347i	−0.281128	+	1.95529i	0.0142166	+	0.999899i	$0.495475\pi$
$53$	−2.04664	+	14.2347i	−0.281128	+	1.95529i	−0.295345	+	0.955391i	$0.595435\pi$
$54$		0			0
$55$	0.553242	+	0.355547i	0.0745991	+	0.0479419i
$56$		0			0
$57$	1.61909	+	3.54531i	0.214453	+	0.469587i
$58$		0			0
$59$	−0.584927	−	4.06826i	−0.0761511	−	0.529642i	−0.991814	−	0.127694i	$-0.959242\pi$
$59$	−0.584927	−	4.06826i	−0.0761511	−	0.529642i	0.915663	−	0.401948i	$-0.131667\pi$
$60$		0			0
$61$	−6.83371	+	2.00656i	−0.874967	+	0.256914i	−0.688227	−	0.725496i	$-0.741611\pi$
$61$	−6.83371	+	2.00656i	−0.874967	+	0.256914i	−0.186741	+	0.982409i	$0.559792\pi$
$62$		0			0
$63$	1.90267	−	2.19580i	0.239714	−	0.276645i
$64$		0			0
$65$	1.87778	+	2.16708i	0.232910	+	0.268793i
$66$		0			0
$67$	1.66308	−	3.64163i	0.203177	−	0.444896i	−0.780425	−	0.625250i	$-0.784997\pi$
$67$	1.66308	−	3.64163i	0.203177	−	0.444896i	0.983602	+	0.180354i	$0.0577243\pi$
$68$		0			0
$69$	−3.74319	+	1.63815i	−0.450627	+	0.197210i
$70$		0			0
$71$	2.94055	−	6.43891i	0.348979	−	0.764158i	−0.651008	−	0.759071i	$-0.725653\pi$
$71$	2.94055	−	6.43891i	0.348979	−	0.764158i	0.999987	−	0.00508708i	$-0.00161927\pi$
$72$		0			0
$73$	2.53968	+	2.93095i	0.297247	+	0.343042i	0.884652	−	0.466251i	$-0.154396\pi$
$73$	2.53968	+	2.93095i	0.297247	+	0.343042i	−0.587405	+	0.809293i	$0.699850\pi$
$74$		0			0
$75$	2.44425	−	2.82082i	0.282238	−	0.325720i
$76$		0			0
$77$	−0.263212	+	0.0772860i	−0.0299958	+	0.00880756i
$78$		0			0
$79$	−1.92588	−	13.3948i	−0.216678	−	1.50703i	−0.750182	−	0.661232i	$-0.770034\pi$
$79$	−1.92588	−	13.3948i	−0.216678	−	1.50703i	0.533504	−	0.845798i	$-0.320875\pi$
$80$		0			0
$81$	1.24378	+	2.72350i	0.138198	+	0.302611i
$82$		0			0
$83$	8.81386	+	5.66433i	0.967447	+	0.621741i	0.926049	−	0.377402i	$-0.123183\pi$
$83$	8.81386	+	5.66433i	0.967447	+	0.621741i	0.0413978	+	0.999143i	$0.486819\pi$
$84$		0			0
$85$	1.10422	−	7.68000i	0.119769	−	0.833013i
$86$		0			0
$87$	−1.50052	+	0.964324i	−0.160872	+	0.103386i
$88$		0			0
$89$	4.62819	+	1.35896i	0.490587	+	0.144049i	0.517664	−	0.855584i	$-0.326802\pi$
$89$	4.62819	+	1.35896i	0.490587	+	0.144049i	−0.0270770	+	0.999633i	$0.508620\pi$
$90$		0			0
$91$	−1.19611			−0.125387
$92$		0			0
$93$	−6.19767			−0.642668
$94$		0			0
$95$	13.4439	+	3.94748i	1.37931	+	0.405002i
$96$		0			0
$97$	9.77480	−	6.28188i	0.992481	−	0.637829i	0.0596787	−	0.998218i	$-0.480992\pi$
$97$	9.77480	−	6.28188i	0.992481	−	0.637829i	0.932802	+	0.360389i	$0.117356\pi$
$98$		0			0
$99$	0.0694913	−	0.483322i	0.00698414	−	0.0485757i
$100$		0			0
$101$	14.0411	+	9.02369i	1.39714	+	0.897890i	0.999804	−	0.0197809i	$-0.00629688\pi$
$101$	14.0411	+	9.02369i	1.39714	+	0.897890i	0.397340	+	0.917671i	$0.369933\pi$
$102$		0			0
$103$	0.832916	+	1.82383i	0.0820697	+	0.179708i	0.946218	−	0.323530i	$-0.104870\pi$
$103$	0.832916	+	1.82383i	0.0820697	+	0.179708i	−0.864148	+	0.503237i	$0.832142\pi$
$104$		0			0
$105$	0.474462	+	3.29996i	0.0463028	+	0.322043i
$106$		0			0
$107$	3.16458	−	0.929204i	0.305931	−	0.0898295i	−0.125164	−	0.992136i	$-0.539946\pi$
$107$	3.16458	−	0.929204i	0.305931	−	0.0898295i	0.431095	+	0.902307i	$0.358127\pi$
$108$		0			0
$109$	0.314835	−	0.363339i	0.0301557	−	0.0348016i	−0.740471	−	0.672088i	$-0.765398\pi$
$109$	0.314835	−	0.363339i	0.0301557	−	0.0348016i	0.770627	+	0.637286i	$0.219943\pi$
$110$		0			0
$111$	−5.75358	−	6.63998i	−0.546105	−	0.630239i
$112$		0			0
$113$	1.23410	−	2.70231i	0.116095	−	0.254212i	−0.842660	−	0.538445i	$-0.819012\pi$
$113$	1.23410	−	2.70231i	0.116095	−	0.254212i	0.958755	+	0.284234i	$0.0917391\pi$
$114$		0			0
$115$	−4.36153	+	14.0264i	−0.406715	+	1.30797i
$116$		0			0
$117$	0.884446	−	1.93667i	0.0817670	−	0.179045i
$118$		0			0
$119$	2.11948	+	2.44601i	0.194292	+	0.224225i
$120$		0			0
$121$	7.17328	−	8.27840i	0.652116	−	0.752582i
$122$		0			0
$123$	4.35629	−	1.27912i	0.392793	−	0.115334i
$124$		0			0
$125$	0.269836	+	1.87675i	0.0241349	+	0.167862i
$126$		0			0
$127$	6.03876	+	13.2230i	0.535853	+	1.17335i	0.963081	+	0.269211i	$0.0867629\pi$
$127$	6.03876	+	13.2230i	0.535853	+	1.17335i	−0.427228	+	0.904144i	$0.640510\pi$
$128$		0			0
$129$	−6.92202	−	4.44851i	−0.609450	−	0.391670i
$130$		0			0
$131$	2.67418	−	18.5993i	0.233644	−	1.62503i	−0.448479	−	0.893793i	$-0.648034\pi$
$131$	2.67418	−	18.5993i	0.233644	−	1.62503i	0.682123	−	0.731237i	$-0.261057\pi$
$132$		0			0
$133$	−4.91683	+	3.15986i	−0.426343	+	0.273994i
$134$		0			0
$135$	−13.2052	−	3.87740i	−1.13652	−	0.333713i
$136$		0			0
$137$	−20.9794			−1.79239			−0.896197	−	0.443657i	$-0.853681\pi$
$137$	−20.9794			−1.79239			−0.896197	+	0.443657i	$0.853681\pi$
$138$		0			0
$139$	−13.7231			−1.16398			−0.581991	−	0.813195i	$-0.697726\pi$
$139$	−13.7231			−1.16398			−0.581991	+	0.813195i	$0.697726\pi$
$140$		0			0
$141$	4.37712	+	1.28524i	0.368620	+	0.108237i
$142$		0			0
$143$	−0.169108	+	0.108679i	−0.0141415	+	0.00908822i
$144$		0			0
$145$	−0.912554	+	6.34695i	−0.0757835	+	0.527086i
$146$		0			0
$147$	3.84720	+	2.47244i	0.317311	+	0.203924i
$148$		0			0
$149$	−3.84541	−	8.42027i	−0.315028	−	0.689815i	0.684192	−	0.729302i	$-0.260155\pi$
$149$	−3.84541	−	8.42027i	−0.315028	−	0.689815i	−0.999220	+	0.0394868i	$0.987428\pi$
$150$		0			0
$151$	−1.14815	−	7.98559i	−0.0934354	−	0.649858i	−0.981687	−	0.190501i	$-0.938989\pi$
$151$	−1.14815	−	7.98559i	−0.0934354	−	0.649858i	0.888252	−	0.459357i	$-0.151920\pi$
$152$		0			0
$153$	−5.52762	+	1.62306i	−0.446882	+	0.131216i
$154$		0			0
$155$	−14.5905	+	16.8384i	−1.17194	+	1.35249i
$156$		0			0
$157$	−1.89961	−	2.19227i	−0.151606	−	0.174962i	0.674867	−	0.737940i	$-0.264201\pi$
$157$	−1.89961	−	2.19227i	−0.151606	−	0.174962i	−0.826472	+	0.562978i	$0.809656\pi$
$158$		0			0
$159$	−5.08983	+	11.1452i	−0.403650	+	0.883870i
$160$		0			0
$161$	−3.23038	−	5.20648i	−0.254590	−	0.410328i
$162$		0			0
$163$	−9.42959	+	20.6479i	−0.738583	+	1.61727i	0.0472888	+	0.998881i	$0.484942\pi$
$163$	−9.42959	+	20.6479i	−0.738583	+	1.61727i	−0.785872	+	0.618390i	$0.787785\pi$
$164$		0			0
$165$	0.366915	+	0.423443i	0.0285643	+	0.0329650i
$166$		0			0
$167$	13.2667	−	15.3106i	1.02661	−	1.18477i	0.0440081	−	0.999031i	$-0.485987\pi$
$167$	13.2667	−	15.3106i	1.02661	−	1.18477i	0.982599	−	0.185737i	$-0.0594673\pi$
$168$		0			0
$169$	11.6324	−	3.41559i	0.894802	−	0.262738i
$170$		0			0
$171$	−1.48056	−	10.2975i	−0.113221	−	0.787469i
$172$		0			0
$173$	3.50720	+	7.67969i	0.266647	+	0.583876i	0.994835	−	0.101501i	$-0.0323646\pi$
$173$	3.50720	+	7.67969i	0.266647	+	0.583876i	−0.728188	+	0.685377i	$0.759637\pi$
$174$		0			0
$175$	4.70863	+	3.02605i	0.355939	+	0.228748i
$176$		0			0
$177$	0.498346	−	3.46607i	0.0374580	−	0.260526i
$178$		0			0
$179$	15.1054	−	9.70767i	1.12903	−	0.725585i	0.163674	−	0.986514i	$-0.447665\pi$
$179$	15.1054	−	9.70767i	1.12903	−	0.725585i	0.965358	+	0.260929i	$0.0840290\pi$
$180$		0			0
$181$	4.22286	+	1.23994i	0.313882	+	0.0921642i	0.434879	−	0.900489i	$-0.356791\pi$
$181$	4.22286	+	1.23994i	0.313882	+	0.0921642i	−0.120997	+	0.992653i	$0.538609\pi$
$182$		0			0
$183$	−6.06798			−0.448558
$184$		0			0
$185$	−31.5852			−2.32219
$186$		0			0
$187$	0.521900	+	0.153244i	0.0381651	+	0.0112063i
$188$		0			0
$189$	4.82954	−	3.10376i	0.351298	−	0.225765i
$190$		0			0
$191$	−2.18842	+	15.2208i	−0.158349	+	1.10134i	0.743328	+	0.668928i	$0.233246\pi$
$191$	−2.18842	+	15.2208i	−0.158349	+	1.10134i	−0.901676	+	0.432412i	$0.857663\pi$
$192$		0			0
$193$	10.8363	+	6.96406i	0.780013	+	0.501284i	0.869038	−	0.494746i	$-0.164739\pi$
$193$	10.8363	+	6.96406i	0.780013	+	0.501284i	−0.0890250	+	0.996029i	$0.528375\pi$
$194$		0			0
$195$	1.01486	+	2.22224i	0.0726759	+	0.159138i
$196$		0			0
$197$	−0.371997	−	2.58730i	−0.0265037	−	0.184337i	0.972269	−	0.233865i	$-0.0751374\pi$
$197$	−0.371997	−	2.58730i	−0.0265037	−	0.184337i	−0.998773	+	0.0495278i	$0.984228\pi$
$198$		0			0
$199$	−17.4615	+	5.12714i	−1.23781	+	0.363454i	−0.834192	−	0.551474i	$-0.814066\pi$
$199$	−17.4615	+	5.12714i	−1.23781	+	0.363454i	−0.403617	+	0.914928i	$0.632247\pi$
$200$		0			0
$201$	2.23361	−	2.57773i	0.157547	−	0.181819i
$202$		0			0
$203$	−1.75159	−	2.02145i	−0.122938	−	0.141878i
$204$		0			0
$205$	6.78034	−	14.8469i	0.473559	−	1.03695i
$206$		0			0
$207$	10.8186	−	1.38057i	0.751946	−	0.0959564i
$208$		0			0
$209$	−0.408043	+	0.893489i	−0.0282249	+	0.0618039i
$210$		0			0
$211$	−4.55158	−	5.25281i	−0.313344	−	0.361618i	0.577130	−	0.816652i	$-0.304173\pi$
$211$	−4.55158	−	5.25281i	−0.313344	−	0.361618i	−0.890474	+	0.455034i	$0.849627\pi$
$212$		0			0
$213$	3.94934	−	4.55778i	0.270604	−	0.312294i
$214$		0			0
$215$	−28.3820	+	8.33370i	−1.93563	+	0.568353i
$216$		0			0
$217$	−1.32266	−	9.19932i	−0.0897881	−	0.624490i
$218$		0			0
$219$	1.37259	+	3.00556i	0.0927512	+	0.203097i
$220$		0			0
$221$	1.99518	+	1.28222i	0.134210	+	0.0862516i
$222$		0			0
$223$	−1.98436	+	13.8015i	−0.132883	+	0.924219i	0.808888	+	0.587963i	$0.200070\pi$
$223$	−1.98436	+	13.8015i	−0.132883	+	0.924219i	−0.941771	+	0.336256i	$0.890839\pi$
$224$		0			0
$225$	−8.38129	+	5.38632i	−0.558752	+	0.359088i
$226$		0			0
$227$	−10.2991	−	3.02408i	−0.683574	−	0.200715i	−0.0785350	−	0.996911i	$-0.525024\pi$
$227$	−10.2991	−	3.02408i	−0.683574	−	0.200715i	−0.605039	+	0.796196i	$0.706842\pi$
$228$		0			0
$229$	−5.31107			−0.350965			−0.175483	−	0.984483i	$-0.556149\pi$
$229$	−5.31107			−0.350965			−0.175483	+	0.984483i	$0.556149\pi$
$230$		0			0
$231$	−0.233718			−0.0153775
$232$		0			0
$233$	5.68951	+	1.67059i	0.372732	+	0.109444i	0.462733	−	0.886498i	$-0.346869\pi$
$233$	5.68951	+	1.67059i	0.372732	+	0.109444i	−0.0900010	+	0.995942i	$0.528687\pi$
$234$		0			0
$235$	13.7965	−	8.86646i	0.899983	−	0.578384i
$236$		0			0
$237$	1.64081	−	11.4121i	0.106582	−	0.741293i
$238$		0			0
$239$	16.1486	+	10.3781i	1.04457	+	0.671301i	0.946112	−	0.323840i	$-0.104974\pi$
$239$	16.1486	+	10.3781i	1.04457	+	0.671301i	0.0984534	+	0.995142i	$0.468610\pi$
$240$		0			0
$241$	−5.02220	−	10.9971i	−0.323508	−	0.708384i	0.676087	−	0.736822i	$-0.263674\pi$
$241$	−5.02220	−	10.9971i	−0.323508	−	0.708384i	−0.999596	+	0.0284371i	$0.990947\pi$
$242$		0			0
$243$	2.28148	+	15.8681i	0.146357	+	1.01794i
$244$		0			0
$245$	15.7744	−	4.63179i	1.00779	−	0.295914i
$246$		0			0
$247$	−2.80467	+	3.23676i	−0.178457	+	0.205950i
$248$		0			0
$249$	5.84544	+	6.74600i	0.370440	+	0.427510i
$250$		0			0
$251$	−0.853487	+	1.86888i	−0.0538716	+	0.117962i	−0.934654	−	0.355560i	$-0.884290\pi$
$251$	−0.853487	+	1.86888i	−0.0538716	+	0.117962i	0.880782	+	0.473522i	$0.157018\pi$
$252$		0			0
$253$	−0.929778	−	0.442586i	−0.0584546	−	0.0278251i
$254$		0			0
$255$	2.74610	−	6.01311i	0.171967	−	0.376556i
$256$		0			0
$257$	−7.19600	−	8.30462i	−0.448874	−	0.518028i	0.485541	−	0.874214i	$-0.338623\pi$
$257$	−7.19600	−	8.30462i	−0.448874	−	0.518028i	−0.934415	+	0.356186i	$0.884077\pi$
$258$		0			0
$259$	8.62797	−	9.95720i	0.536116	−	0.618711i
$260$		0			0
$261$	4.56817	−	1.34134i	0.282763	−	0.0830266i
$262$		0			0
$263$	−2.58595	−	17.9857i	−0.159457	−	1.10904i	−0.899638	−	0.436637i	$-0.856169\pi$
$263$	−2.58595	−	17.9857i	−0.159457	−	1.10904i	0.740181	−	0.672408i	$-0.234740\pi$
$264$		0			0
$265$	18.2978	+	40.0665i	1.12402	+	2.46126i
$266$		0			0
$267$	3.45720	+	2.22181i	0.211577	+	0.135973i
$268$		0			0
$269$	1.08848	−	7.57056i	0.0663660	−	0.461585i	−0.929356	−	0.369185i	$-0.879637\pi$
$269$	1.08848	−	7.57056i	0.0663660	−	0.461585i	0.995722	−	0.0924005i	$-0.0294540\pi$
$270$		0			0
$271$	22.1011	−	14.2035i	1.34255	−	0.862804i	0.345414	−	0.938450i	$-0.387738\pi$
$271$	22.1011	−	14.2035i	1.34255	−	0.862804i	0.997135	+	0.0756463i	$0.0241020\pi$
$272$		0			0
$273$	−0.977785	−	0.287104i	−0.0591783	−	0.0173763i
$274$		0			0
$275$	0.940660			0.0567239
$276$		0			0
$277$	−6.45543			−0.387869			−0.193935	−	0.981014i	$-0.562125\pi$
$277$	−6.45543			−0.387869			−0.193935	+	0.981014i	$0.562125\pi$
$278$		0			0
$279$	15.8729	+	4.66071i	0.950287	+	0.279029i
$280$		0			0
$281$	15.8457	−	10.1834i	0.945273	−	0.607490i	0.0253875	−	0.999678i	$-0.491918\pi$
$281$	15.8457	−	10.1834i	0.945273	−	0.607490i	0.919885	+	0.392188i	$0.128282\pi$
$282$		0			0
$283$	−1.21577	+	8.45586i	−0.0722700	+	0.502649i	0.921248	+	0.388975i	$0.127171\pi$
$283$	−1.21577	+	8.45586i	−0.0722700	+	0.502649i	−0.993518	+	0.113674i	$0.963738\pi$
$284$		0			0
$285$	10.0424	+	6.45387i	0.594861	+	0.382294i
$286$		0			0
$287$	2.82831	+	6.19314i	0.166950	+	0.365569i
$288$		0			0
$289$	1.50605	+	10.4748i	0.0885914	+	0.616167i
$290$		0			0
$291$	9.49843	−	2.78899i	0.556808	−	0.163494i
$292$		0			0
$293$	−7.92115	+	9.14150i	−0.462759	+	0.534052i	−0.938383	−	0.345596i	$-0.887677\pi$
$293$	−7.92115	+	9.14150i	−0.462759	+	0.534052i	0.475625	+	0.879648i	$0.342222\pi$
$294$		0			0
$295$	−8.24374	−	9.51378i	−0.479969	−	0.553914i
$296$		0			0
$297$	0.400799	−	0.877627i	0.0232567	−	0.0509251i
$298$		0			0
$299$	−3.34614	−	2.99376i	−0.193512	−	0.173134i
$300$		0			0
$301$	5.12577	−	11.2239i	0.295444	−	0.646933i
$302$		0			0
$303$	9.31222	+	10.7469i	0.534973	+	0.617392i
$304$		0			0
$305$	−14.2852	+	16.4860i	−0.817970	+	0.943988i
$306$		0			0
$307$	24.6469	−	7.23697i	1.40667	−	0.413036i	0.511701	−	0.859163i	$-0.329015\pi$
$307$	24.6469	−	7.23697i	1.40667	−	0.413036i	0.894969	+	0.446128i	$0.147197\pi$
$308$		0			0
$309$	0.243107	+	1.69085i	0.0138299	+	0.0961891i
$310$		0			0
$311$	−12.7221	−	27.8575i	−0.721405	−	1.57966i	−0.811925	−	0.583762i	$-0.801580\pi$
$311$	−12.7221	−	27.8575i	−0.721405	−	1.57966i	0.0905202	−	0.995895i	$-0.471147\pi$
$312$		0			0
$313$	−22.3933	−	14.3913i	−1.26574	−	0.813444i	−0.276685	−	0.960961i	$-0.589236\pi$
$313$	−22.3933	−	14.3913i	−1.26574	−	0.813444i	−0.989060	+	0.147516i	$0.952872\pi$
$314$		0			0
$315$	1.26645	−	8.80836i	0.0713564	−	0.496295i
$316$		0			0
$317$	−2.74808	+	1.76608i	−0.154347	+	0.0991931i	−0.615535	−	0.788110i	$-0.711060\pi$
$317$	−2.74808	+	1.76608i	−0.154347	+	0.0991931i	0.461187	+	0.887303i	$0.347424\pi$
$318$		0			0
$319$	−0.431312	−	0.126645i	−0.0241488	−	0.00709074i
$320$		0			0
$321$	2.80998			0.156838
$322$		0			0
$323$	11.5888			0.644821
$324$		0			0
$325$	3.93535	+	1.15552i	0.218294	+	0.0640969i
$326$		0			0
$327$	0.344580	−	0.221448i	0.0190553	−	0.0122461i
$328$		0			0
$329$	−0.973571	+	6.77134i	−0.0536747	+	0.373316i
$330$		0			0
$331$	−23.5588	−	15.1403i	−1.29491	−	0.832188i	−0.302261	−	0.953225i	$-0.597742\pi$
$331$	−23.5588	−	15.1403i	−1.29491	−	0.832188i	−0.992648	+	0.121037i	$0.961378\pi$
$332$		0			0
$333$	9.74222	+	21.3325i	0.533870	+	1.16901i
$334$		0			0
$335$	−1.74503	−	12.1370i	−0.0953414	−	0.663114i
$336$		0			0
$337$	12.5077	−	3.67259i	0.681337	−	0.200059i	0.0772919	−	0.997009i	$-0.475373\pi$
$337$	12.5077	−	3.67259i	0.681337	−	0.200059i	0.604046	+	0.796950i	$0.293554\pi$
$338$		0			0
$339$	1.65748	−	1.91283i	0.0900217	−	0.103891i
$340$		0			0
$341$	−1.02285	−	1.18043i	−0.0553905	−	0.0639241i
$342$		0			0
$343$	−6.56403	+	14.3732i	−0.354424	+	0.776081i
$344$		0			0
$345$	−6.93216	+	10.4192i	−0.373215	+	0.560951i
$346$		0			0
$347$	−12.4894	+	27.3479i	−0.670464	+	1.46811i	0.201977	+	0.979390i	$0.435263\pi$
$347$	−12.4894	+	27.3479i	−0.670464	+	1.46811i	−0.872441	+	0.488720i	$0.837464\pi$
$348$		0			0
$349$	−7.00288	−	8.08175i	−0.374855	−	0.432606i	0.536707	−	0.843769i	$-0.319668\pi$
$349$	−7.00288	−	8.08175i	−0.374855	−	0.432606i	−0.911562	+	0.411163i	$0.865123\pi$
$350$		0			0
$351$	2.75488	−	3.17930i	0.147044	−	0.169698i
$352$		0			0
$353$	−31.3397	+	9.20215i	−1.66804	+	0.489781i	−0.973311	−	0.229489i	$-0.926294\pi$
$353$	−31.3397	+	9.20215i	−1.66804	+	0.489781i	−0.694730	+	0.719270i	$0.744476\pi$
$354$		0			0
$355$	−3.08546	−	21.4599i	−0.163759	−	1.13897i
$356$		0			0
$357$	1.14549	+	2.50827i	0.0606258	+	0.132752i
$358$		0			0
$359$	−11.6822	−	7.50772i	−0.616565	−	0.396242i	0.194749	−	0.980853i	$-0.437611\pi$
$359$	−11.6822	−	7.50772i	−0.616565	−	0.396242i	−0.811314	+	0.584611i	$0.801247\pi$
$360$		0			0
$361$	−0.274317	+	1.90791i	−0.0144377	+	0.100417i
$362$		0			0
$363$	7.85099	−	5.04553i	0.412070	−	0.264821i
$364$		0			0
$365$	11.3971	+	3.34650i	0.596553	+	0.175164i
$366$		0			0
$367$	−8.70583			−0.454441			−0.227220	−	0.973843i	$-0.572964\pi$
$367$	−8.70583			−0.454441			−0.227220	+	0.973843i	$0.572964\pi$
$368$		0			0
$369$	−12.1188			−0.630882
$370$		0			0
$371$	−17.6292	−	5.17641i	−0.915264	−	0.268746i
$372$		0			0
$373$	−0.779682	+	0.501071i	−0.0403704	+	0.0259445i	−0.560670	−	0.828039i	$-0.689457\pi$
$373$	−0.779682	+	0.501071i	−0.0403704	+	0.0259445i	0.520300	+	0.853984i	$0.325820\pi$
$374$		0			0
$375$	−0.229895	+	1.59895i	−0.0118717	+	0.0825697i
$376$		0			0
$377$	−1.64887	−	1.05966i	−0.0849209	−	0.0545754i
$378$		0			0
$379$	13.3906	+	29.3212i	0.687827	+	1.50613i	0.854132	+	0.520056i	$0.174089\pi$
$379$	13.3906	+	29.3212i	0.687827	+	1.50613i	−0.166306	+	0.986074i	$0.553184\pi$
$380$		0			0
$381$	1.76256	+	12.2589i	0.0902988	+	0.628042i
$382$		0			0
$383$	−9.56563	+	2.80872i	−0.488781	+	0.143519i	−0.516831	−	0.856087i	$-0.672888\pi$
$383$	−9.56563	+	2.80872i	−0.488781	+	0.143519i	0.0280499	+	0.999607i	$0.491070\pi$
$384$		0			0
$385$	−0.550220	+	0.634987i	−0.0280418	+	0.0323620i
$386$		0			0
$387$	14.3827	+	16.5986i	0.731116	+	0.843753i
$388$		0			0
$389$	13.7724	−	30.1572i	0.698286	−	1.52903i	−0.143751	−	0.989614i	$-0.545917\pi$
$389$	13.7724	−	30.1572i	0.698286	−	1.52903i	0.842037	−	0.539419i	$-0.181356\pi$
$390$		0			0
$391$	−0.192858	+	12.1476i	−0.00975324	+	0.614330i
$392$		0			0
$393$	6.65046	−	14.5625i	0.335471	−	0.734579i
$394$		0			0
$395$	−27.1426	−	31.3242i	−1.36569	−	1.57609i
$396$		0			0
$397$	−11.1983	+	12.9235i	−0.562024	+	0.648610i	−0.963642	−	0.267197i	$-0.913903\pi$
$397$	−11.1983	+	12.9235i	−0.562024	+	0.648610i	0.401618	+	0.915807i	$0.368448\pi$
$398$		0			0
$399$	−4.77781	+	1.40289i	−0.239190	+	0.0702325i
$400$		0			0
$401$	3.09765	+	21.5446i	0.154689	+	1.07589i	0.908226	+	0.418481i	$0.137437\pi$
$401$	3.09765	+	21.5446i	0.154689	+	1.07589i	−0.753536	+	0.657406i	$0.771654\pi$
$402$		0			0
$403$	−2.82914	−	6.19496i	−0.140930	−	0.308593i
$404$		0			0
$405$	7.71458	+	4.95786i	0.383340	+	0.246358i
$406$		0			0
$407$	0.315119	−	2.19170i	0.0156199	−	0.108639i
$408$		0			0
$409$	−28.4862	+	18.3070i	−1.40855	+	0.905223i	−0.999972	−	0.00749867i	$-0.997613\pi$
$409$	−28.4862	+	18.3070i	−1.40855	+	0.905223i	−0.408582	+	0.912721i	$0.633977\pi$
$410$		0			0
$411$	−17.1500	−	5.03570i	−0.845948	−	0.248393i
$412$		0			0
$413$	5.25111			0.258390
$414$		0			0
$415$	32.0895			1.57521
$416$		0			0
$417$	−11.2182	−	3.29397i	−0.549359	−	0.161306i
$418$		0			0
$419$	2.00403	−	1.28791i	0.0979030	−	0.0629185i	−0.490773	−	0.871287i	$-0.663286\pi$
$419$	2.00403	−	1.28791i	0.0979030	−	0.0629185i	0.588676	+	0.808369i	$0.299649\pi$
$420$		0			0
$421$	−3.64913	+	25.3803i	−0.177848	+	1.23696i	0.683883	+	0.729592i	$0.260290\pi$
$421$	−3.64913	+	25.3803i	−0.177848	+	1.23696i	−0.861731	+	0.507366i	$0.830619\pi$
$422$		0			0
$423$	−10.2438	−	6.58328i	−0.498070	−	0.320090i
$424$		0			0
$425$	−4.61032	−	10.0952i	−0.223634	−	0.489689i
$426$		0			0
$427$	−1.29498	−	9.00681i	−0.0626687	−	0.435870i
$428$		0			0
$429$	−0.164327	+	0.0482507i	−0.00793378	+	0.00232957i
$430$		0			0
$431$	−0.0218038	+	0.0251629i	−0.00105025	+	0.00121206i	−0.756274	−	0.654254i	$-0.772983\pi$
$431$	−0.0218038	+	0.0251629i	−0.00105025	+	0.00121206i	0.755224	+	0.655467i	$0.227528\pi$
$432$		0			0
$433$	0.783279	+	0.903952i	0.0376420	+	0.0434412i	0.774258	−	0.632870i	$-0.218123\pi$
$433$	0.783279	+	0.903952i	0.0376420	+	0.0434412i	−0.736616	+	0.676311i	$0.763578\pi$
$434$		0			0
$435$	−2.26944	+	4.96939i	−0.108812	+	0.238264i
$436$		0			0
$437$	−21.6637	−	3.46662i	−1.03632	−	0.165831i
$438$		0			0
$439$	6.41264	−	14.0417i	0.306059	−	0.670175i	−0.692634	−	0.721289i	$-0.743550\pi$
$439$	6.41264	−	14.0417i	0.306059	−	0.670175i	0.998693	+	0.0511142i	$0.0162772\pi$
$440$		0			0
$441$	−7.99380	−	9.22533i	−0.380657	−	0.439302i
$442$		0			0
$443$	−4.63685	+	5.35121i	−0.220304	+	0.254244i	−0.855133	−	0.518408i	$-0.826525\pi$
$443$	−4.63685	+	5.35121i	−0.220304	+	0.254244i	0.634830	+	0.772652i	$0.281070\pi$
$444$		0			0
$445$	14.1754	−	4.16226i	0.671977	−	0.197310i
$446$		0			0
$447$	−1.12238	−	7.80631i	−0.0530867	−	0.369226i
$448$		0			0
$449$	−4.02515	−	8.81386i	−0.189959	−	0.415952i	0.790558	−	0.612387i	$-0.209791\pi$
$449$	−4.02515	−	8.81386i	−0.189959	−	0.415952i	−0.980517	+	0.196436i	$0.937063\pi$
$450$		0			0
$451$	0.962581	+	0.618613i	0.0453262	+	0.0291294i
$452$		0			0
$453$	0.978203	−	6.80355i	0.0459600	−	0.319659i
$454$		0			0
$455$	−3.08193	+	1.98064i	−0.144483	+	0.0928537i
$456$		0			0
$457$	−13.4522	−	3.94992i	−0.629266	−	0.184769i	−0.0484785	−	0.998824i	$-0.515437\pi$
$457$	−13.4522	−	3.94992i	−0.629266	−	0.184769i	−0.580788	+	0.814055i	$0.697255\pi$
$458$		0			0
$459$	−11.3831			−0.531318
$460$		0			0
$461$	−0.854133			−0.0397809			−0.0198905	−	0.999802i	$-0.506332\pi$
$461$	−0.854133			−0.0397809			−0.0198905	+	0.999802i	$0.506332\pi$
$462$		0			0
$463$	6.67547	+	1.96010i	0.310236	+	0.0910934i	0.433144	−	0.901325i	$-0.357404\pi$
$463$	6.67547	+	1.96010i	0.310236	+	0.0910934i	−0.122909	+	0.992418i	$0.539222\pi$
$464$		0			0
$465$	−15.9690	+	10.2627i	−0.740546	+	0.475920i
$466$		0			0
$467$	−4.10379	+	28.5425i	−0.189901	+	1.32079i	0.642360	+	0.766403i	$0.277956\pi$
$467$	−4.10379	+	28.5425i	−0.189901	+	1.32079i	−0.832260	+	0.554385i	$0.812954\pi$
$468$		0			0
$469$	4.30285	+	2.76528i	0.198687	+	0.127689i
$470$		0			0
$471$	−1.02666	−	2.24807i	−0.0473061	−	0.103586i
$472$		0			0
$473$	−0.295115	−	2.05257i	−0.0135694	−	0.0943774i
$474$		0			0
$475$	19.2295	−	5.64630i	0.882312	−	0.259070i
$476$		0			0
$477$	21.4169	−	24.7164i	0.980613	−	1.13169i
$478$		0			0
$479$	2.39860	+	2.76814i	0.109595	+	0.126479i	0.807897	−	0.589324i	$-0.200606\pi$
$479$	2.39860	+	2.76814i	0.109595	+	0.126479i	−0.698302	+	0.715804i	$0.746061\pi$
$480$		0			0
$481$	4.01066	−	8.78212i	0.182870	−	0.400430i
$482$		0			0
$483$	−1.39102	−	5.03152i	−0.0632937	−	0.228942i
$484$		0			0
$485$	14.7838	−	32.3720i	0.671299	−	1.46994i
$486$		0			0
$487$	20.3349	+	23.4677i	0.921463	+	1.06342i	0.997797	+	0.0663425i	$0.0211330\pi$
$487$	20.3349	+	23.4677i	0.921463	+	1.06342i	−0.0763341	+	0.997082i	$0.524322\pi$
$488$		0			0
$489$	−12.6645	+	14.6156i	−0.572709	+	0.660942i
$490$		0			0
$491$	18.5161	−	5.43682i	0.835620	−	0.245360i	0.164190	−	0.986429i	$-0.447499\pi$
$491$	18.5161	−	5.43682i	0.835620	−	0.245360i	0.671429	+	0.741069i	$0.265681\pi$
$492$		0			0
$493$	0.754773	+	5.24956i	0.0339933	+	0.236428i
$494$		0			0
$495$	−0.621278	−	1.36041i	−0.0279243	−	0.0611458i
$496$		0			0
$497$	7.60804	+	4.88939i	0.341267	+	0.219319i
$498$		0			0
$499$	−4.26024	+	29.6306i	−0.190714	+	1.32645i	0.639409	+	0.768867i	$0.279179\pi$
$499$	−4.26024	+	29.6306i	−0.190714	+	1.32645i	−0.830123	+	0.557580i	$0.811730\pi$
$500$		0			0
$501$	14.5201	−	9.33150i	0.648710	−	0.416901i
$502$		0			0
$503$	4.42136	+	1.29823i	0.197139	+	0.0578852i	0.378811	−	0.925474i	$-0.376333\pi$
$503$	4.42136	+	1.29823i	0.197139	+	0.0578852i	−0.181673	+	0.983359i	$0.558151\pi$
$504$		0			0
$505$	51.1209			2.27485
$506$		0			0
$507$	10.3290			0.458726
$508$		0			0
$509$	−3.92130	−	1.15140i	−0.173809	−	0.0510349i	0.193670	−	0.981067i	$-0.437961\pi$
$509$	−3.92130	−	1.15140i	−0.173809	−	0.0510349i	−0.367479	+	0.930032i	$0.619779\pi$
$510$		0			0
$511$	−4.16828	+	2.67879i	−0.184394	+	0.118503i
$512$		0			0
$513$	2.92543	−	20.3468i	0.129161	−	0.898333i
$514$		0			0
$515$	5.16618	+	3.32010i	0.227649	+	0.146301i
$516$		0			0
$517$	0.477601	+	1.04580i	0.0210048	+	0.0459942i
$518$		0			0
$519$	1.02366	+	7.11973i	0.0449338	+	0.312522i
$520$		0			0
$521$	−4.28290	+	1.25757i	−0.187637	+	0.0550953i	−0.374201	−	0.927348i	$-0.622083\pi$
$521$	−4.28290	+	1.25757i	−0.187637	+	0.0550953i	0.186564	+	0.982443i	$0.440265\pi$
$522$		0			0
$523$	−9.47424	+	10.9339i	−0.414280	+	0.478104i	−0.924086	−	0.382185i	$-0.875172\pi$
$523$	−9.47424	+	10.9339i	−0.414280	+	0.478104i	0.509806	+	0.860289i	$0.329717\pi$
$524$		0			0
$525$	3.12281	+	3.60391i	0.136291	+	0.157288i
$526$		0			0
$527$	−7.65531	+	16.7628i	−0.333470	+	0.730198i
$528$		0			0
$529$	3.99428	−	22.6505i	0.173664	−	0.984805i
$530$		0			0
$531$	−3.88284	+	8.50223i	−0.168501	+	0.368966i
$532$		0			0
$533$	3.26714	+	3.77048i	0.141516	+	0.163318i
$534$		0			0
$535$	6.61525	−	7.63440i	0.286002	−	0.330064i
$536$		0			0
$537$	14.6783	−	4.30995i	0.633417	−	0.185988i
$538$		0			0
$539$	0.164022	+	1.14080i	0.00706495	+	0.0491378i
$540$		0			0
$541$	1.34391	+	2.94275i	0.0577791	+	0.126519i	0.936319	−	0.351150i	$-0.114209\pi$
$541$	1.34391	+	2.94275i	0.0577791	+	0.126519i	−0.878540	+	0.477669i	$0.841482\pi$
$542$		0			0
$543$	3.15443	+	2.02723i	0.135369	+	0.0869966i
$544$		0			0
$545$	0.209560	−	1.45752i	0.00897655	−	0.0624333i
$546$		0			0
$547$	2.73914	−	1.76034i	0.117117	−	0.0752667i	−0.480771	−	0.876846i	$-0.659643\pi$
$547$	2.73914	−	1.76034i	0.117117	−	0.0752667i	0.597888	+	0.801580i	$0.296007\pi$
$548$		0			0
$549$	15.5408	+	4.56318i	0.663264	+	0.194752i
$550$		0			0
$551$	−9.57732			−0.408008
$552$		0			0
$553$	17.2893			0.735216
$554$		0			0
$555$	−25.8199	−	7.58140i	−1.09599	−	0.321813i
$556$		0			0
$557$	−9.12124	+	5.86187i	−0.386479	+	0.248375i	−0.719424	−	0.694571i	$-0.755594\pi$
$557$	−9.12124	+	5.86187i	−0.386479	+	0.248375i	0.332945	+	0.942946i	$0.391958\pi$
$558$		0			0
$559$	1.28677	−	8.94968i	0.0544246	−	0.378531i
$560$		0			0
$561$	0.389854	+	0.250544i	0.0164596	+	0.0105780i
$562$		0			0
$563$	2.15378	+	4.71611i	0.0907709	+	0.198760i	0.949572	−	0.313548i	$-0.101518\pi$
$563$	2.15378	+	4.71611i	0.0907709	+	0.198760i	−0.858801	+	0.512309i	$0.828790\pi$
$564$		0			0
$565$	−1.29492	−	9.00636i	−0.0544777	−	0.378901i
$566$		0			0
$567$	−3.67031	+	1.07770i	−0.154139	+	0.0452592i
$568$		0			0
$569$	17.8093	−	20.5530i	0.746604	−	0.861627i	−0.247631	−	0.968854i	$-0.579652\pi$
$569$	17.8093	−	20.5530i	0.746604	−	0.861627i	0.994234	+	0.107228i	$0.0341974\pi$
$570$		0			0
$571$	0.258462	+	0.298281i	0.0108163	+	0.0124827i	0.761132	−	0.648597i	$-0.224644\pi$
$571$	0.258462	+	0.298281i	0.0108163	+	0.0124827i	−0.750316	+	0.661080i	$0.770098\pi$
$572$		0			0
$573$	−5.44242	+	11.9172i	−0.227360	+	0.497850i
$574$		0			0
$575$	5.59852	+	20.2506i	0.233475	+	0.844510i
$576$		0			0
$577$	−2.45463	+	5.37489i	−0.102188	+	0.223760i	−0.953819	−	0.300381i	$-0.902886\pi$
$577$	−2.45463	+	5.37489i	−0.102188	+	0.223760i	0.851632	+	0.524141i	$0.175613\pi$
$578$		0			0
$579$	7.18673	+	8.29393i	0.298670	+	0.344684i
$580$		0			0
$581$	−8.76572	+	10.1162i	−0.363663	+	0.419690i
$582$		0			0
$583$	−2.96277	+	0.869949i	−0.122706	+	0.0360296i
$584$		0			0
$585$	−0.928031	−	6.45460i	−0.0383694	−	0.266865i
$586$		0			0
$587$	−14.7226	−	32.2381i	−0.607669	−	1.33061i	−0.924157	−	0.382013i	$-0.875231\pi$
$587$	−14.7226	−	32.2381i	−0.607669	−	1.33061i	0.316488	−	0.948596i	$-0.397496\pi$
$588$		0			0
$589$	−27.9953	−	17.9915i	−1.15353	−	0.741326i
$590$		0			0
$591$	0.316934	−	2.20432i	0.0130369	−	0.0906738i
$592$		0			0
$593$	25.6347	−	16.4744i	1.05269	−	0.676524i	0.104598	−	0.994515i	$-0.466644\pi$
$593$	25.6347	−	16.4744i	1.05269	−	0.676524i	0.948094	+	0.317991i	$0.103008\pi$
$594$		0			0
$595$	9.51143	+	2.79281i	0.389930	+	0.114494i
$596$		0			0
$597$	−15.5048			−0.634571
$598$		0			0
$599$	22.6521			0.925539			0.462770	−	0.886479i	$-0.346856\pi$
$599$	22.6521			0.925539			0.462770	+	0.886479i	$0.346856\pi$
$600$		0			0
$601$	14.1372	+	4.15104i	0.576666	+	0.169325i	0.557044	−	0.830483i	$-0.311935\pi$
$601$	14.1372	+	4.15104i	0.576666	+	0.169325i	0.0196223	+	0.999807i	$0.493754\pi$
$602$		0			0
$603$	−7.65901	+	4.92215i	−0.311899	+	0.200445i
$604$		0			0
$605$	4.77466	−	33.2085i	0.194117	−	1.35012i
$606$		0			0
$607$	−33.7455	−	21.6869i	−1.36969	−	0.880244i	−0.370861	−	0.928689i	$-0.620937\pi$
$607$	−33.7455	−	21.6869i	−1.36969	−	0.880244i	−0.998826	+	0.0484446i	$0.984574\pi$
$608$		0			0
$609$	−0.946663	−	2.07290i	−0.0383607	−	0.0839983i
$610$		0			0
$611$	0.713414	+	4.96190i	0.0288616	+	0.200737i
$612$		0			0
$613$	−26.2068	+	7.69500i	−1.05848	+	0.310798i	−0.764239	−	0.644933i	$-0.776885\pi$
$613$	−26.2068	+	7.69500i	−1.05848	+	0.310798i	−0.294242	+	0.955731i	$0.595067\pi$
$614$		0			0
$615$	9.10641	−	10.5094i	0.367206	−	0.423778i
$616$		0			0
$617$	7.75272	+	8.94711i	0.312113	+	0.360197i	0.890033	−	0.455896i	$-0.150681\pi$
$617$	7.75272	+	8.94711i	0.312113	+	0.360197i	−0.577920	+	0.816093i	$0.696136\pi$
$618$		0			0
$619$	4.18050	−	9.15401i	0.168028	−	0.367931i	−0.806821	−	0.590796i	$-0.798814\pi$
$619$	4.18050	−	9.15401i	0.168028	−	0.367931i	0.974849	+	0.222865i	$0.0715410\pi$
$620$		0			0
$621$	21.2791	+	3.40508i	0.853901	+	0.136641i
$622$		0			0
$623$	−2.56006	+	5.60576i	−0.102567	+	0.224590i
$624$		0			0
$625$	18.1475	+	20.9434i	0.725901	+	0.837734i
$626$		0			0
$627$	−0.548026	+	0.632456i	−0.0218861	+	0.0252579i
$628$		0			0
$629$	−25.0659	+	7.36001i	−0.999442	+	0.293463i
$630$		0			0
$631$	4.01100	+	27.8971i	0.159675	+	1.11057i	0.899232	+	0.437472i	$0.144126\pi$
$631$	4.01100	+	27.8971i	0.159675	+	1.11057i	−0.739557	+	0.673094i	$0.764965\pi$
$632$		0			0
$633$	−2.45994	−	5.38652i	−0.0977739	−	0.214095i
$634$		0			0
$635$	37.4555	+	24.0712i	1.48638	+	0.955236i
$636$		0			0
$637$	−0.715175	+	4.97415i	−0.0283363	+	0.197083i
$638$		0			0
$639$	−13.5422	+	8.70304i	−0.535721	+	0.344287i
$640$		0			0
$641$	30.9702	+	9.09367i	1.22325	+	0.359178i	0.828698	−	0.559696i	$-0.189082\pi$
$641$	30.9702	+	9.09367i	1.22325	+	0.359178i	0.394551	+	0.918874i	$0.370900\pi$
$642$		0			0
$643$	37.3247			1.47194			0.735971	−	0.677013i	$-0.236726\pi$
$643$	37.3247			1.47194			0.735971	+	0.677013i	$0.236726\pi$
$644$		0			0
$645$	−25.2017			−0.992315
$646$		0			0
$647$	24.0258	+	7.05462i	0.944552	+	0.277346i	0.717517	−	0.696541i	$-0.245279\pi$
$647$	24.0258	+	7.05462i	0.944552	+	0.277346i	0.227035	+	0.973887i	$0.427097\pi$
$648$		0			0
$649$	0.742409	−	0.477117i	0.0291421	−	0.0187285i
$650$		0			0
$651$	1.12688	−	7.83762i	0.0441659	−	0.307181i
$652$		0			0
$653$	−11.2051	−	7.20110i	−0.438491	−	0.281801i	0.302712	−	0.953082i	$-0.402108\pi$
$653$	−11.2051	−	7.20110i	−0.438491	−	0.281801i	−0.741203	+	0.671281i	$0.765744\pi$
$654$		0			0
$655$	−23.9081	−	52.3515i	−0.934169	−	2.04554i
$656$		0			0
$657$	−1.25515	−	8.72977i	−0.0489681	−	0.340581i
$658$		0			0
$659$	19.6457	−	5.76848i	0.765286	−	0.224708i	0.124283	−	0.992247i	$-0.460337\pi$
$659$	19.6457	−	5.76848i	0.765286	−	0.224708i	0.641003	+	0.767539i	$0.278519\pi$
$660$		0			0
$661$	−13.5785	+	15.6705i	−0.528143	+	0.609510i	−0.955651	−	0.294502i	$-0.904846\pi$
$661$	−13.5785	+	15.6705i	−0.528143	+	0.609510i	0.427507	+	0.904012i	$0.359392\pi$
$662$		0			0
$663$	1.32322	+	1.52708i	0.0513896	+	0.0593068i
$664$		0			0
$665$	−7.43642	+	16.2835i	−0.288372	+	0.631447i
$666$		0			0
$667$	0.159383	−	10.0391i	0.00617133	−	0.388715i
$668$		0			0
$669$	−4.93493	+	10.8060i	−0.190796	+	0.417784i
$670$		0			0
$671$	−1.00145	−	1.15573i	−0.0386605	−	0.0446166i
$672$		0			0
$673$	7.73728	−	8.92930i	0.298250	−	0.344199i	−0.586768	−	0.809755i	$-0.699600\pi$
$673$	7.73728	−	8.92930i	0.298250	−	0.344199i	0.885019	+	0.465556i	$0.154145\pi$
$674$		0			0
$675$	−18.8882	+	5.54607i	−0.727006	+	0.213468i
$676$		0			0
$677$	3.92414	+	27.2930i	0.150817	+	1.04895i	0.914855	+	0.403783i	$0.132305\pi$
$677$	3.92414	+	27.2930i	0.150817	+	1.04895i	−0.764038	+	0.645171i	$0.776786\pi$
$678$		0			0
$679$	6.16684	+	13.5035i	0.236662	+	0.518217i
$680$		0			0
$681$	−7.69329	−	4.94418i	−0.294808	−	0.189461i
$682$		0			0
$683$	1.33135	−	9.25976i	0.0509428	−	0.354315i	−0.948367	−	0.317174i	$-0.897266\pi$
$683$	1.33135	−	9.25976i	0.0509428	−	0.354315i	0.999310	−	0.0371406i	$-0.0118249\pi$
$684$		0			0
$685$	−54.0560	+	34.7397i	−2.06537	+	1.32734i
$686$		0			0
$687$	−4.34163	−	1.27482i	−0.165643	−	0.0486373i
$688$		0			0
$689$	−13.4637			−0.512927
$690$		0			0
$691$	−25.0171			−0.951696			−0.475848	−	0.879528i	$-0.657859\pi$
$691$	−25.0171			−0.951696			−0.475848	+	0.879528i	$0.657859\pi$
$692$		0			0
$693$	0.598579	+	0.175759i	0.0227381	+	0.00667652i
$694$		0			0
$695$	−35.3593	+	22.7241i	−1.34126	+	0.861973i
$696$		0			0
$697$	1.92122	−	13.3624i	0.0727714	−	0.506136i
$698$		0			0
$699$	4.25000	+	2.73131i	0.160750	+	0.103308i
$700$		0			0
$701$	0.688924	+	1.50853i	0.0260203	+	0.0569765i	0.922196	−	0.386723i	$-0.126393\pi$
$701$	0.688924	+	1.50853i	0.0260203	+	0.0569765i	−0.896176	+	0.443699i	$0.853666\pi$
$702$		0			0
$703$	−6.71381	−	46.6956i	−0.253216	−	1.76116i
$704$		0			0
$705$	13.4064	−	3.93647i	0.504914	−	0.148256i
$706$		0			0
$707$	−13.9644	+	16.1158i	−0.525187	+	0.606098i
$708$		0			0
$709$	−23.1676	−	26.7368i	−0.870078	−	1.00412i	−0.999921	−	0.0125888i	$-0.995993\pi$
$709$	−23.1676	−	26.7368i	−0.870078	−	1.00412i	0.129843	−	0.991535i	$-0.458553\pi$
$710$		0			0
$711$	−12.7843	+	27.9937i	−0.479448	+	1.04984i
$712$		0			0
$713$	19.3248	−	29.0457i	0.723721	−	1.08777i
$714$		0			0
$715$	−0.255766	+	0.560050i	−0.00956512	+	0.0209447i
$716$		0			0
$717$	10.7099	+	12.3599i	0.399969	+	0.461588i
$718$		0			0
$719$	1.12354	−	1.29663i	0.0419009	−	0.0483563i	−0.734412	−	0.678704i	$-0.762542\pi$
$719$	1.12354	−	1.29663i	0.0419009	−	0.0483563i	0.776313	+	0.630347i	$0.217088\pi$
$720$		0			0
$721$	−2.45788	+	0.721698i	−0.0915361	+	0.0268774i
$722$		0			0
$723$	−1.46585	−	10.1952i	−0.0545157	−	0.379165i
$724$		0			0
$725$	3.81009	+	8.34294i	0.141503	+	0.309849i
$726$		0			0
$727$	15.5564	+	9.99747i	0.576954	+	0.370786i	0.796337	−	0.604853i	$-0.206768\pi$
$727$	15.5564	+	9.99747i	0.576954	+	0.370786i	−0.219383	+	0.975639i	$0.570405\pi$
$728$		0			0
$729$	−0.665474	+	4.62847i	−0.0246472	+	0.171425i
$730$		0			0
$731$	−20.5819	+	13.2272i	−0.761249	+	0.489225i
$732$		0			0
$733$	−19.4340	−	5.70635i	−0.717813	−	0.210769i	−0.0976263	−	0.995223i	$-0.531125\pi$
$733$	−19.4340	−	5.70635i	−0.717813	−	0.210769i	−0.620187	+	0.784454i	$0.712943\pi$
$734$		0			0
$735$	14.0069			0.516651
$736$		0			0
$737$	0.859597			0.0316637
$738$		0			0
$739$	−45.2056	−	13.2736i	−1.66292	−	0.488276i	−0.690853	−	0.722995i	$-0.742765\pi$
$739$	−45.2056	−	13.2736i	−1.66292	−	0.488276i	−0.972063	+	0.234719i	$0.924583\pi$
$740$		0			0
$741$	−3.06965	+	1.97274i	−0.112766	+	0.0724705i
$742$		0			0
$743$	6.44028	−	44.7931i	0.236271	−	1.64330i	−0.433805	−	0.901007i	$-0.642829\pi$
$743$	6.44028	−	44.7931i	0.236271	−	1.64330i	0.670075	−	0.742293i	$-0.266262\pi$
$744$		0			0
$745$	−23.8512	−	15.3282i	−0.873841	−	0.561583i
$746$		0			0
$747$	−9.89777	−	21.6731i	−0.362140	−	0.792977i
$748$		0			0
$749$	0.599685	+	4.17090i	0.0219120	+	0.152401i
$750$		0			0
$751$	−39.0441	+	11.4644i	−1.42474	+	0.418341i	−0.901105	−	0.433602i	$-0.857242\pi$
$751$	−39.0441	+	11.4644i	−1.42474	+	0.418341i	−0.523634	+	0.851943i	$0.675424\pi$
$752$		0			0
$753$	−1.14628	+	1.32288i	−0.0417729	+	0.0482085i
$754$		0			0
$755$	−16.1816	−	18.6746i	−0.588910	−	0.679638i
$756$		0			0
$757$	6.01044	−	13.1610i	0.218453	−	0.478346i	−0.768399	−	0.639971i	$-0.778946\pi$
$757$	6.01044	−	13.1610i	0.218453	−	0.478346i	0.986852	+	0.161625i	$0.0516736\pi$
$758$		0			0
$759$	−0.653830	−	0.584974i	−0.0237325	−	0.0212332i
$760$		0			0
$761$	−13.7044	+	30.0084i	−0.496782	+	1.08780i	0.480719	+	0.876875i	$0.340376\pi$
$761$	−13.7044	+	30.0084i	−0.496782	+	1.08780i	−0.977502	+	0.210927i	$0.932352\pi$
$762$		0			0
$763$	0.402237	+	0.464207i	0.0145620	+	0.0168054i
$764$		0			0
$765$	−11.5550	+	13.3352i	−0.417771	+	0.482133i
$766$		0			0
$767$	3.69204	−	1.08408i	0.133312	−	0.0391439i
$768$		0			0
$769$	7.07162	+	49.1842i	0.255009	+	1.77363i	0.567173	+	0.823599i	$0.308037\pi$
$769$	7.07162	+	49.1842i	0.255009	+	1.77363i	−0.312164	+	0.950028i	$0.601054\pi$
$770$		0			0
$771$	−3.88914	−	8.51602i	−0.140064	−	0.306697i
$772$		0			0
$773$	11.4533	+	7.36059i	0.411947	+	0.264742i	0.730159	−	0.683278i	$-0.239446\pi$
$773$	11.4533	+	7.36059i	0.411947	+	0.264742i	−0.318212	+	0.948020i	$0.603082\pi$
$774$		0			0
$775$	−4.53542	+	31.5445i	−0.162917	+	1.13311i
$776$		0			0
$777$	9.44312	−	6.06872i	0.338770	−	0.217714i
$778$		0			0
$779$	23.3909	+	6.86818i	0.838065	+	0.246078i
$780$		0			0
$781$	1.51989			0.0543858
$782$		0			0
$783$	9.40730			0.336189
$784$		0			0
$785$	−8.52474	−	2.50309i	−0.304261	−	0.0893391i
$786$		0			0
$787$	2.11128	−	1.35684i	0.0752592	−	0.0483661i	−0.502470	−	0.864595i	$-0.667575\pi$
$787$	2.11128	−	1.35684i	0.0752592	−	0.0483661i	0.577729	+	0.816228i	$0.303939\pi$
$788$		0			0
$789$	2.20318	−	15.3234i	0.0784351	−	0.545528i
$790$		0			0
$791$	3.19297	+	2.05200i	0.113529	+	0.0729607i
$792$		0			0
$793$	−2.76994	−	6.06532i	−0.0983635	−	0.215386i
$794$		0			0
$795$	5.34066	+	37.1451i	0.189414	+	1.31740i
$796$		0			0
$797$	−20.7587	+	6.09530i	−0.735311	+	0.215907i	−0.627885	−	0.778306i	$-0.716079\pi$
$797$	−20.7587	+	6.09530i	−0.735311	+	0.215907i	−0.107426	+	0.994213i	$0.534261\pi$
$798$		0			0
$799$	8.88276	−	10.2513i	0.314250	−	0.362663i
$800$		0			0
$801$	−7.18346	−	8.29016i	−0.253815	−	0.292918i
$802$		0			0
$803$	−0.345921	+	0.757462i	−0.0122073	+	0.0267303i
$804$		0			0
$805$	−16.9448	−	8.06595i	−0.597227	−	0.284287i
$806$		0			0
$807$	2.70696	−	5.92743i	0.0952897	−	0.208655i
$808$		0			0
$809$	25.2910	+	29.1873i	0.889183	+	1.02617i	0.999479	+	0.0322726i	$0.0102745\pi$
$809$	25.2910	+	29.1873i	0.889183	+	1.02617i	−0.110297	+	0.993899i	$0.535180\pi$
$810$		0			0
$811$	17.9636	−	20.7311i	0.630788	−	0.727969i	−0.346930	−	0.937891i	$-0.612776\pi$
$811$	17.9636	−	20.7311i	0.630788	−	0.727969i	0.977718	+	0.209923i	$0.0673212\pi$
$812$		0			0
$813$	21.4763	−	6.30600i	0.753205	−	0.221161i
$814$		0			0
$815$	9.89428	+	68.8163i	0.346582	+	2.41053i
$816$		0			0
$817$	−18.3535	−	40.1885i	−0.642107	−	1.40602i
$818$		0			0
$819$	2.28831	+	1.47061i	0.0799601	+	0.0513872i
$820$		0			0
$821$	−2.64575	+	18.4016i	−0.0923374	+	0.642221i	0.890119	+	0.455728i	$0.150621\pi$
$821$	−2.64575	+	18.4016i	−0.0923374	+	0.642221i	−0.982456	+	0.186492i	$0.940288\pi$
$822$		0			0
$823$	31.3972	−	20.1778i	1.09444	−	0.703353i	0.136590	−	0.990628i	$-0.456386\pi$
$823$	31.3972	−	20.1778i	1.09444	−	0.703353i	0.957848	+	0.287275i	$0.0927493\pi$
$824$		0			0
$825$	0.768959	+	0.225787i	0.0267717	+	0.00786089i
$826$		0			0
$827$	19.9983			0.695409			0.347704	−	0.937604i	$-0.386961\pi$
$827$	19.9983			0.695409			0.347704	+	0.937604i	$0.386961\pi$
$828$		0			0
$829$	31.7857			1.10396			0.551982	−	0.833856i	$-0.313872\pi$
$829$	31.7857			1.10396			0.551982	+	0.833856i	$0.313872\pi$
$830$		0			0
$831$	−5.27711	−	1.54950i	−0.183061	−	0.0537515i
$832$		0			0
$833$	11.4392	−	7.35154i	0.396346	−	0.254716i
$834$		0			0
$835$	8.83054	−	61.4178i	0.305593	−	2.12545i
$836$		0			0
$837$	27.4983	+	17.6721i	0.950481	+	0.610837i
$838$		0			0
$839$	−9.12250	−	19.9755i	−0.314944	−	0.689631i	0.684272	−	0.729227i	$-0.260120\pi$
$839$	−9.12250	−	19.9755i	−0.314944	−	0.689631i	−0.999216	+	0.0395962i	$0.987393\pi$
$840$		0			0
$841$	3.50337	+	24.3664i	0.120806	+	0.840222i
$842$		0			0
$843$	15.3976	−	4.52115i	0.530323	−	0.155717i
$844$		0			0
$845$	24.3165	−	28.0627i	0.836512	−	0.965387i
$846$		0			0
$847$	9.16467	+	10.5766i	0.314902	+	0.363416i
$848$		0			0
$849$	−3.02352	+	6.62058i	−0.103767	+	0.227218i
$850$		0			0
$851$	49.0587	−	6.26042i	1.68171	−	0.214605i
$852$		0			0
$853$	−21.7166	+	47.5526i	−0.743561	+	1.62817i	0.0340455	+	0.999420i	$0.489161\pi$
$853$	−21.7166	+	47.5526i	−0.743561	+	1.62817i	−0.777607	+	0.628751i	$0.783566\pi$
$854$		0			0
$855$	−20.8664	−	24.0811i	−0.713615	−	0.823555i
$856$		0			0
$857$	12.7263	−	14.6869i	0.434722	−	0.501696i	−0.495544	−	0.868583i	$-0.665031\pi$
$857$	12.7263	−	14.6869i	0.434722	−	0.501696i	0.930265	+	0.366887i	$0.119577\pi$
$858$		0			0
$859$	13.3259	−	3.91284i	0.454674	−	0.133504i	−0.0463733	−	0.998924i	$-0.514766\pi$
$859$	13.3259	−	3.91284i	0.454674	−	0.133504i	0.501047	+	0.865420i	$0.332948\pi$
$860$		0			0
$861$	0.825514	+	5.74157i	0.0281334	+	0.195672i
$862$		0			0
$863$	−8.72736	−	19.1103i	−0.297083	−	0.650521i	0.700950	−	0.713210i	$-0.252760\pi$
$863$	−8.72736	−	19.1103i	−0.297083	−	0.650521i	−0.998033	+	0.0626894i	$0.980032\pi$
$864$		0			0
$865$	21.7534	+	13.9801i	0.739639	+	0.475337i
$866$		0			0
$867$	−1.28313	+	8.92434i	−0.0435773	+	0.303087i
$868$		0			0
$869$	2.44439	−	1.57091i	0.0829201	−	0.0532895i
$870$		0			0
$871$	3.59621	+	1.05594i	0.121853	+	0.0357793i
$872$		0			0
$873$	−26.4239			−0.894313
$874$		0			0
$875$	−2.42242			−0.0818928
$876$		0			0
$877$	−27.8078	−	8.16509i	−0.939001	−	0.275716i	−0.223801	−	0.974635i	$-0.571846\pi$
$877$	−27.8078	−	8.16509i	−0.939001	−	0.275716i	−0.715200	+	0.698919i	$0.753665\pi$
$878$		0			0
$879$	−8.66953	+	5.57157i	−0.292416	+	0.187924i
$880$		0			0
$881$	1.19897	−	8.33903i	0.0403944	−	0.280949i	−0.959606	−	0.281349i	$-0.909218\pi$
$881$	1.19897	−	8.33903i	0.0403944	−	0.280949i	1.00000		0.000399892i	$0.000127290\pi$
$882$		0			0
$883$	−7.97555	−	5.12557i	−0.268399	−	0.172489i	0.399518	−	0.916725i	$-0.369177\pi$
$883$	−7.97555	−	5.12557i	−0.268399	−	0.172489i	−0.667917	+	0.744236i	$0.732814\pi$
$884$		0			0
$885$	−4.45540	−	9.75596i	−0.149766	−	0.327943i
$886$		0			0
$887$	0.00756554	+	0.0526195i	0.000254026	+	0.00176679i	0.989948	−	0.141431i	$-0.0451705\pi$
$887$	0.00756554	+	0.0526195i	0.000254026	+	0.00176679i	−0.989694	+	0.143198i	$0.954261\pi$
$888$		0			0
$889$	−17.8200	+	5.23241i	−0.597662	+	0.175489i
$890$		0			0
$891$	−0.420993	+	0.485852i	−0.0141038	+	0.0162767i
$892$		0			0
$893$	16.0408	+	18.5121i	0.536785	+	0.619483i
$894$		0			0
$895$	22.8461	−	50.0259i	0.763660	−	1.67218i
$896$		0			0
$897$	−2.01677	−	3.25048i	−0.0673381	−	0.108530i
$898$		0			0
$899$	6.32654	−	13.8532i	0.211002	−	0.462030i
$900$		0			0
$901$	23.8574	+	27.5329i	0.794804	+	0.917252i
$902$		0			0
$903$	6.88422	−	7.94481i	0.229092	−	0.264387i
$904$		0			0
$905$	12.9339	−	3.79774i	0.429938	−	0.126241i
$906$		0			0
$907$	−1.65663	−	11.5221i	−0.0550077	−	0.382587i	−0.998665	−	0.0516615i	$-0.983548\pi$
$907$	−1.65663	−	11.5221i	−0.0550077	−	0.382587i	0.943657	−	0.330925i	$-0.107361\pi$
$908$		0			0
$909$	−15.7679	−	34.5268i	−0.522987	−	1.14518i
$910$		0			0
$911$	18.6436	+	11.9815i	0.617691	+	0.396966i	0.811734	−	0.584027i	$-0.198524\pi$
$911$	18.6436	+	11.9815i	0.617691	+	0.396966i	−0.194043	+	0.980993i	$0.562160\pi$
$912$		0			0
$913$	−0.320150	+	2.22670i	−0.0105954	+	0.0736929i
$914$		0			0
$915$	−15.6349	+	10.0479i	−0.516873	+	0.332174i
$916$		0			0
$917$	23.0346	+	6.76358i	0.760671	+	0.223353i
$918$		0			0
$919$	6.37804			0.210392			0.105196	−	0.994451i	$-0.466453\pi$
$919$	6.37804			0.210392			0.105196	+	0.994451i	$0.466453\pi$
$920$		0			0
$921$	21.8851			0.721139
$922$		0			0
$923$	6.35861	+	1.86706i	0.209296	+	0.0614549i
$924$		0			0
$925$	−38.0063	+	24.4251i	−1.24964	+	0.803094i
$926$		0			0
$927$	0.648911	−	4.51327i	0.0213130	−	0.148235i
$928$		0			0
$929$	7.02396	+	4.51402i	0.230449	+	0.148100i	0.650770	−	0.759275i	$-0.274446\pi$
$929$	7.02396	+	4.51402i	0.230449	+	0.148100i	−0.420321	+	0.907375i	$0.638083\pi$
$930$		0			0
$931$	10.2007	+	22.3364i	0.334314	+	0.732046i
$932$		0			0
$933$	−3.71327	−	25.8263i	−0.121567	−	0.845516i
$934$		0			0
$935$	1.59849	−	0.469360i	0.0522763	−	0.0153497i
$936$		0			0
$937$	−23.2527	+	26.8350i	−0.759632	+	0.876662i	−0.995465	−	0.0951315i	$-0.969673\pi$
$937$	−23.2527	+	26.8350i	−0.759632	+	0.876662i	0.235833	+	0.971794i	$0.424218\pi$
$938$		0			0
$939$	−14.8515	−	17.1395i	−0.484659	−	0.559326i
$940$		0			0
$941$	−17.2715	+	37.8192i	−0.563033	+	1.23287i	0.387391	+	0.921916i	$0.373376\pi$
$941$	−17.2715	+	37.8192i	−0.563033	+	1.23287i	−0.950424	+	0.310956i	$0.899351\pi$
$942$		0			0
$943$	−7.58859	+	24.4044i	−0.247119	+	0.794715i
$944$		0			0
$945$	7.30440	−	15.9944i	0.237612	−	0.520298i
$946$		0			0
$947$	−9.41531	−	10.8658i	−0.305956	−	0.353092i	0.581861	−	0.813288i	$-0.302325\pi$
$947$	−9.41531	−	10.8658i	−0.305956	−	0.353092i	−0.887818	+	0.460196i	$0.847779\pi$
$948$		0			0
$949$	−2.37768	+	2.74399i	−0.0771827	+	0.0890736i
$950$		0			0
$951$	−2.67038	+	0.784094i	−0.0865930	+	0.0254260i
$952$		0			0
$953$	−1.92224	−	13.3695i	−0.0622676	−	0.433081i	−0.996979	−	0.0776728i	$-0.975251\pi$
$953$	−1.92224	−	13.3695i	−0.0622676	−	0.433081i	0.934711	−	0.355408i	$-0.115658\pi$
$954$		0			0
$955$	19.5653	+	42.8420i	0.633118	+	1.38634i
$956$		0			0
$957$	−0.322185	−	0.207056i	−0.0104148	−	0.00669316i
$958$		0			0
$959$	3.81455	−	26.5308i	0.123178	−	0.856723i
$960$		0			0
$961$	18.4381	−	11.8494i	0.594777	−	0.382240i
$962$		0			0
$963$	−7.19666	−	2.11313i	−0.231909	−	0.0680947i
$964$		0			0
$965$	39.4527			1.27003
$966$		0			0
$967$	20.6391			0.663709			0.331855	−	0.943331i	$-0.392326\pi$
$967$	20.6391			0.663709			0.331855	+	0.943331i	$0.392326\pi$
$968$		0			0
$969$	9.47351	+	2.78167i	0.304333	+	0.0893602i
$970$		0			0
$971$	−35.2773	+	22.6713i	−1.13210	+	0.727558i	−0.965998	−	0.258551i	$-0.916755\pi$
$971$	−35.2773	+	22.6713i	−1.13210	+	0.727558i	−0.166104	+	0.986108i	$0.553119\pi$
$972$		0			0
$973$	2.49519	−	17.3544i	0.0799921	−	0.556357i
$974$		0			0
$975$	2.93966	+	1.88921i	0.0941445	+	0.0605030i
$976$		0			0
$977$	−5.15187	−	11.2810i	−0.164823	−	0.360912i	0.809141	−	0.587615i	$-0.199933\pi$
$977$	−5.15187	−	11.2810i	−0.164823	−	0.360912i	−0.973964	+	0.226702i	$0.927206\pi$
$978$		0			0
$979$	0.147395	+	1.02516i	0.00471078	+	0.0327642i
$980$		0			0
$981$	−1.04904	+	0.308026i	−0.0334932	+	0.00983450i
$982$		0			0
$983$	24.3582	−	28.1109i	0.776907	−	0.896598i	−0.219975	−	0.975506i	$-0.570598\pi$
$983$	24.3582	−	28.1109i	0.776907	−	0.896598i	0.996882	+	0.0789071i	$0.0251430\pi$
$984$		0			0
$985$	−5.24278	−	6.05050i	−0.167049	−	0.192785i
$986$		0			0
$987$	−2.42119	+	5.30166i	−0.0770673	+	0.168754i
$988$		0			0
$989$	42.4316	−	18.5696i	1.34925	−	0.590478i
$990$		0			0
$991$	8.00306	−	17.5243i	0.254226	−	0.556677i	−0.738888	−	0.673828i	$-0.764649\pi$
$991$	8.00306	−	17.5243i	0.254226	−	0.556677i	0.993114	+	0.117151i	$0.0373762\pi$
$992$		0			0
$993$	−15.6244	−	18.0316i	−0.495826	−	0.572214i
$994$		0			0
$995$	−36.5015	+	42.1250i	−1.15718	+	1.33545i
$996$		0			0
$997$	16.5154	−	4.84936i	0.523048	−	0.153581i	−0.00954163	−	0.999954i	$-0.503037\pi$
$997$	16.5154	−	4.84936i	0.523048	−	0.153581i	0.532589	+	0.846374i	$0.321219\pi$
$998$		0			0
$999$	6.59463	+	45.8666i	0.208645	+	1.45116i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	184.2.i.b.121.2	yes	30
4.3	odd	2		368.2.m.e.305.2		30
23.2	even	11		4232.2.a.bb.1.6		15
23.4	even	11	inner	184.2.i.b.73.2	✓	30
23.21	odd	22		4232.2.a.ba.1.6		15
92.27	odd	22		368.2.m.e.257.2		30
92.67	even	22		8464.2.a.ch.1.10		15
92.71	odd	22		8464.2.a.cg.1.10		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.2.i.b.73.2	✓	30	23.4	even	11	inner
184.2.i.b.121.2	yes	30	1.1	even	1	trivial
368.2.m.e.257.2		30	92.27	odd	22
368.2.m.e.305.2		30	4.3	odd	2
4232.2.a.ba.1.6		15	23.21	odd	22
4232.2.a.bb.1.6		15	23.2	even	11
8464.2.a.cg.1.10		15	92.71	odd	22
8464.2.a.ch.1.10		15	92.67	even	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 184 = 2^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	184.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.817468 + 0.240030i) q^{3} +(2.57662 - 1.65589i) q^{5} +(-0.181823 + 1.26461i) q^{7} +(-1.91312 - 1.22949i) q^{9} +O(q^{10})\)	\(q+(0.817468 + 0.240030i) q^{3} +(2.57662 - 1.65589i) q^{5} +(-0.181823 + 1.26461i) q^{7} +(-1.91312 - 1.22949i) q^{9} +(0.0891963 + 0.195313i) q^{11} +(0.133237 + 0.926681i) q^{13} +(2.50377 - 0.735173i) q^{15} +(1.65894 - 1.91452i) q^{17} +(2.99577 + 3.45730i) q^{19} +(-0.452179 + 0.990134i) q^{21} +(-3.67385 + 3.08267i) q^{23} +(1.81991 - 3.98505i) q^{25} +(-2.94258 - 3.39592i) q^{27} +(-1.37099 + 1.58221i) q^{29} +(-6.97977 + 2.04945i) q^{31} +(0.0260342 + 0.181072i) q^{33} +(1.62557 + 3.55950i) q^{35} +(-8.67535 - 5.57531i) q^{37} +(-0.113515 + 0.789513i) q^{39} +(4.48304 - 2.88108i) q^{41} +(-9.26657 - 2.72091i) q^{43} -6.96529 q^{45} +5.35449 q^{47} +(5.15027 + 1.51226i) q^{49} +(1.81567 - 1.16686i) q^{51} +(-2.04664 + 14.2347i) q^{53} +(0.553242 + 0.355547i) q^{55} +(1.61909 + 3.54531i) q^{57} +(-0.584927 - 4.06826i) q^{59} +(-6.83371 + 2.00656i) q^{61} +(1.90267 - 2.19580i) q^{63} +(1.87778 + 2.16708i) q^{65} +(1.66308 - 3.64163i) q^{67} +(-3.74319 + 1.63815i) q^{69} +(2.94055 - 6.43891i) q^{71} +(2.53968 + 2.93095i) q^{73} +(2.44425 - 2.82082i) q^{75} +(-0.263212 + 0.0772860i) q^{77} +(-1.92588 - 13.3948i) q^{79} +(1.24378 + 2.72350i) q^{81} +(8.81386 + 5.66433i) q^{83} +(1.10422 - 7.68000i) q^{85} +(-1.50052 + 0.964324i) q^{87} +(4.62819 + 1.35896i) q^{89} -1.19611 q^{91} -6.19767 q^{93} +(13.4439 + 3.94748i) q^{95} +(9.77480 - 6.28188i) q^{97} +(0.0694913 - 0.483322i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 2 q^{3} - 13 q^{7} + 21 q^{9}+O(q^{10}) \) 30 * q + 2 * q^3 - 13 * q^7 + 21 * q^9	\( 30 q + 2 q^{3} - 13 q^{7} + 21 q^{9} + 2 q^{11} - 2 q^{15} - 22 q^{17} + 3 q^{19} + 2 q^{21} + q^{23} + 13 q^{25} - 31 q^{27} + 7 q^{29} + 18 q^{31} - 8 q^{33} + 41 q^{35} - 62 q^{37} + 6 q^{39} - 15 q^{41} - 47 q^{43} + 8 q^{45} - 72 q^{47} - 16 q^{49} - 7 q^{51} - 43 q^{53} - 9 q^{55} - 42 q^{57} - 11 q^{59} + 57 q^{61} - 62 q^{63} + 14 q^{65} - 27 q^{67} - 22 q^{69} + 48 q^{71} - 12 q^{73} + 87 q^{75} - 3 q^{77} + 8 q^{79} + 123 q^{81} - 18 q^{83} + 54 q^{85} + 137 q^{87} - 23 q^{89} + 142 q^{91} - 110 q^{93} + 119 q^{95} + 47 q^{97} - 17 q^{99}+O(q^{100}) \) 30 * q + 2 * q^3 - 13 * q^7 + 21 * q^9 + 2 * q^11 - 2 * q^15 - 22 * q^17 + 3 * q^19 + 2 * q^21 + q^23 + 13 * q^25 - 31 * q^27 + 7 * q^29 + 18 * q^31 - 8 * q^33 + 41 * q^35 - 62 * q^37 + 6 * q^39 - 15 * q^41 - 47 * q^43 + 8 * q^45 - 72 * q^47 - 16 * q^49 - 7 * q^51 - 43 * q^53 - 9 * q^55 - 42 * q^57 - 11 * q^59 + 57 * q^61 - 62 * q^63 + 14 * q^65 - 27 * q^67 - 22 * q^69 + 48 * q^71 - 12 * q^73 + 87 * q^75 - 3 * q^77 + 8 * q^79 + 123 * q^81 - 18 * q^83 + 54 * q^85 + 137 * q^87 - 23 * q^89 + 142 * q^91 - 110 * q^93 + 119 * q^95 + 47 * q^97 - 17 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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