LMFDB - Embedded newform 168.2.u.a.89.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(17,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("168.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.u (of order $6$, degree $2$, 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:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 6 x^{15} + 19 x^{14} - 42 x^{13} + 65 x^{12} - 48 x^{11} - 94 x^{10} + 444 x^{9} - 962 x^{8} + \cdots + 6561 $ x^16 - 6x^15 + 19x^14 - 42x^13 + 65x^12 - 48x^11 - 94x^10 + 444x^9 - 962x^8 + 1332x^7 - 846x^6 - 1296x^5 + 5265x^4 - 10206x^3 + 13851x^2 - 13122*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.5
Root			$-0.601642 + 1.62420i$ of defining polynomial
Character	$\chi$	$=$	168.89
Dual form			168.2.u.a.17.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.291063 - 1.70742i) q^{3} +(-0.0726693 + 0.125867i) q^{5} +(1.05451 - 2.42652i) q^{7} +(-2.83056 - 0.993934i) q^{9} +O(q^{10})$	\(q+(0.291063 - 1.70742i) q^{3} +(-0.0726693 + 0.125867i) q^{5} +(1.05451 - 2.42652i) q^{7} +(-2.83056 - 0.993934i) q^{9} +(2.13889 - 1.23489i) q^{11} +2.04143i q^{13} +(0.193756 + 0.160712i) q^{15} +(-0.878419 - 1.52147i) q^{17} +(-3.68319 - 2.12649i) q^{19} +(-3.83616 - 2.50676i) q^{21} +(7.46351 + 4.30906i) q^{23} +(2.48944 + 4.31183i) q^{25} +(-2.52094 + 4.54366i) q^{27} +7.08790i q^{29} +(3.11812 - 1.80025i) q^{31} +(-1.48592 - 4.01141i) q^{33} +(0.228788 + 0.309061i) q^{35} +(-2.93493 + 5.08345i) q^{37} +(3.48558 + 0.594185i) q^{39} +5.33255 q^{41} -9.19692 q^{43} +(0.330798 - 0.284046i) q^{45} +(-4.65190 + 8.05733i) q^{47} +(-4.77602 - 5.11758i) q^{49} +(-2.85346 + 1.05699i) q^{51} +(4.49578 - 2.59564i) q^{53} +0.358953i q^{55} +(-4.70286 + 5.66982i) q^{57} +(-5.60299 - 9.70466i) q^{59} +(4.66353 + 2.69249i) q^{61} +(-5.39666 + 5.82031i) q^{63} +(-0.256949 - 0.148349i) q^{65} +(2.57417 + 4.45860i) q^{67} +(9.52973 - 11.4891i) q^{69} -7.79323i q^{71} +(11.3013 - 6.52482i) q^{73} +(8.08669 - 2.99550i) q^{75} +(-0.741003 - 6.49226i) q^{77} +(2.86075 - 4.95497i) q^{79} +(7.02419 + 5.62679i) q^{81} -15.9818 q^{83} +0.255336 q^{85} +(12.1020 + 2.06303i) q^{87} +(-4.34252 + 7.52147i) q^{89} +(4.95358 + 2.15271i) q^{91} +(-2.16621 - 5.84793i) q^{93} +(0.535310 - 0.309061i) q^{95} -6.65337i q^{97} +(-7.28165 + 1.36951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{7} + 2 q^{9}+O(q^{10}) $ 16 * q + 4 * q^7 + 2 * q^9	$ 16 q + 4 q^{7} + 2 q^{9} + 8 q^{15} - 6 q^{19} + 14 q^{21} - 18 q^{25} - 48 q^{31} - 12 q^{33} - 2 q^{37} - 22 q^{39} + 20 q^{43} - 42 q^{45} - 28 q^{49} + 6 q^{51} - 8 q^{57} + 36 q^{61} - 32 q^{63} + 14 q^{67} + 30 q^{73} + 54 q^{75} + 28 q^{79} + 30 q^{81} + 16 q^{85} + 78 q^{87} + 66 q^{91} + 16 q^{93} + 20 q^{99}+O(q^{100}) $ 16 * q + 4 * q^7 + 2 * q^9 + 8 * q^15 - 6 * q^19 + 14 * q^21 - 18 * q^25 - 48 * q^31 - 12 * q^33 - 2 * q^37 - 22 * q^39 + 20 * q^43 - 42 * q^45 - 28 * q^49 + 6 * q^51 - 8 * q^57 + 36 * q^61 - 32 * q^63 + 14 * q^67 + 30 * q^73 + 54 * q^75 + 28 * q^79 + 30 * q^81 + 16 * q^85 + 78 * q^87 + 66 * q^91 + 16 * q^93 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.291063	−	1.70742i	0.168045	−	0.985779i
$3$	0.291063	−	1.70742i	0.168045	−	0.985779i
$4$		0			0
$5$	−0.0726693	+	0.125867i	−0.0324987	+	0.0562894i	−0.881817	−	0.471591i	$-0.843680\pi$
$5$	−0.0726693	+	0.125867i	−0.0324987	+	0.0562894i	0.849319	+	0.527881i	$0.177013\pi$
$6$		0			0
$7$	1.05451	−	2.42652i	0.398567	−	0.917139i
$7$	1.05451	−	2.42652i	0.398567	−	0.917139i
$8$		0			0
$9$	−2.83056	−	0.993934i	−0.943521	−	0.331311i
$10$		0			0
$11$	2.13889	−	1.23489i	0.644899	−	0.372332i	−0.141600	−	0.989924i	$-0.545225\pi$
$11$	2.13889	−	1.23489i	0.644899	−	0.372332i	0.786499	+	0.617592i	$0.211891\pi$
$12$		0			0
$13$			2.04143i			0.566191i	0.959092	+	0.283096i	$0.0913613\pi$
$13$			2.04143i			0.566191i	−0.959092	+	0.283096i	$0.908639\pi$
$14$		0			0
$15$	0.193756	+	0.160712i	0.0500276	+	0.0414957i
$16$		0			0
$17$	−0.878419	−	1.52147i	−0.213048	−	0.369010i	0.739619	−	0.673026i	$-0.235006\pi$
$17$	−0.878419	−	1.52147i	−0.213048	−	0.369010i	−0.952667	+	0.304016i	$0.901672\pi$
$18$		0			0
$19$	−3.68319	−	2.12649i	−0.844983	−	0.487851i	0.0139720	−	0.999902i	$-0.495552\pi$
$19$	−3.68319	−	2.12649i	−0.844983	−	0.487851i	−0.858955	+	0.512051i	$0.828886\pi$
$20$		0			0
$21$	−3.83616	−	2.50676i	−0.837119	−	0.547020i
$22$		0			0
$23$	7.46351	+	4.30906i	1.55625	+	0.898501i	0.997610	+	0.0690910i	$0.0220099\pi$
$23$	7.46351	+	4.30906i	1.55625	+	0.898501i	0.558640	+	0.829410i	$0.311323\pi$
$24$		0			0
$25$	2.48944	+	4.31183i	0.497888	+	0.862367i
$26$		0			0
$27$	−2.52094	+	4.54366i	−0.485154	+	0.874429i
$28$		0			0
$29$			7.08790i			1.31619i	0.752935	+	0.658095i	$0.228637\pi$
$29$			7.08790i			1.31619i	−0.752935	+	0.658095i	$0.771363\pi$
$30$		0			0
$31$	3.11812	−	1.80025i	0.560031	−	0.323334i	−0.193127	−	0.981174i	$-0.561863\pi$
$31$	3.11812	−	1.80025i	0.560031	−	0.323334i	0.753158	+	0.657840i	$0.228530\pi$
$32$		0			0
$33$	−1.48592	−	4.01141i	−0.258665	−	0.698296i
$34$		0			0
$35$	0.228788	+	0.309061i	0.0386723	+	0.0522409i
$36$		0			0
$37$	−2.93493	+	5.08345i	−0.482499	+	0.835713i	−0.999798	−	0.0200916i	$-0.993604\pi$
$37$	−2.93493	+	5.08345i	−0.482499	+	0.835713i	0.517299	+	0.855805i	$0.326938\pi$
$38$		0			0
$39$	3.48558	+	0.594185i	0.558139	+	0.0951458i
$40$		0			0
$41$	5.33255			0.832804			0.416402	−	0.909181i	$-0.363291\pi$
$41$	5.33255			0.832804			0.416402	+	0.909181i	$0.363291\pi$
$42$		0			0
$43$	−9.19692			−1.40252			−0.701258	−	0.712907i	$-0.747378\pi$
$43$	−9.19692			−1.40252			−0.701258	+	0.712907i	$0.747378\pi$
$44$		0			0
$45$	0.330798	−	0.284046i	0.0493125	−	0.0423431i
$46$		0			0
$47$	−4.65190	+	8.05733i	−0.678549	+	1.17528i	0.296868	+	0.954918i	$0.404058\pi$
$47$	−4.65190	+	8.05733i	−0.678549	+	1.17528i	−0.975418	+	0.220364i	$0.929276\pi$
$48$		0			0
$49$	−4.77602	−	5.11758i	−0.682288	−	0.731083i
$50$		0			0
$51$	−2.85346	+	1.05699i	−0.399564	+	0.148008i
$52$		0			0
$53$	4.49578	−	2.59564i	0.617543	−	0.356539i	−0.158369	−	0.987380i	$-0.550623\pi$
$53$	4.49578	−	2.59564i	0.617543	−	0.356539i	0.775912	+	0.630841i	$0.217290\pi$
$54$		0			0
$55$			0.358953i			0.0484013i
$56$		0			0
$57$	−4.70286	+	5.66982i	−0.622909	+	0.750985i
$58$		0			0
$59$	−5.60299	−	9.70466i	−0.729447	−	1.26344i	−0.957117	−	0.289701i	$-0.906444\pi$
$59$	−5.60299	−	9.70466i	−0.729447	−	1.26344i	0.227670	−	0.973738i	$-0.426889\pi$
$60$		0			0
$61$	4.66353	+	2.69249i	0.597104	+	0.344738i	0.767901	−	0.640568i	$-0.221301\pi$
$61$	4.66353	+	2.69249i	0.597104	+	0.344738i	−0.170798	+	0.985306i	$0.554634\pi$
$62$		0			0
$63$	−5.39666	+	5.82031i	−0.679915	+	0.733291i
$64$		0			0
$65$	−0.256949	−	0.148349i	−0.0318705	−	0.0184005i
$66$		0			0
$67$	2.57417	+	4.45860i	0.314485	+	0.544705i	0.979328	−	0.202279i	$-0.0648347\pi$
$67$	2.57417	+	4.45860i	0.314485	+	0.544705i	−0.664843	+	0.746984i	$0.731501\pi$
$68$		0			0
$69$	9.52973	−	11.4891i	1.14724	−	1.38313i
$70$		0			0
$71$		−	7.79323i		−	0.924886i	−0.886649	−	0.462443i	$-0.846973\pi$
$71$		−	7.79323i		−	0.924886i	0.886649	−	0.462443i	$-0.153027\pi$
$72$		0			0
$73$	11.3013	−	6.52482i	1.32272	−	0.763672i	0.338558	−	0.940946i	$-0.390061\pi$
$73$	11.3013	−	6.52482i	1.32272	−	0.763672i	0.984162	+	0.177273i	$0.0567277\pi$
$74$		0			0
$75$	8.08669	−	2.99550i	0.933771	−	0.345891i
$76$		0			0
$77$	−0.741003	−	6.49226i	−0.0844451	−	0.739861i
$78$		0			0
$79$	2.86075	−	4.95497i	0.321860	−	0.557478i	−0.659012	−	0.752133i	$-0.729025\pi$
$79$	2.86075	−	4.95497i	0.321860	−	0.557478i	0.980872	+	0.194655i	$0.0623586\pi$
$80$		0			0
$81$	7.02419	+	5.62679i	0.780466	+	0.625199i
$82$		0			0
$83$	−15.9818			−1.75423			−0.877115	−	0.480280i	$-0.840535\pi$
$83$	−15.9818			−1.75423			−0.877115	+	0.480280i	$0.840535\pi$
$84$		0			0
$85$	0.255336			0.0276951
$86$		0			0
$87$	12.1020	+	2.06303i	1.29747	+	0.221180i
$88$		0			0
$89$	−4.34252	+	7.52147i	−0.460306	+	0.797274i	−0.998976	−	0.0452432i	$-0.985594\pi$
$89$	−4.34252	+	7.52147i	−0.460306	+	0.797274i	0.538670	+	0.842517i	$0.318927\pi$
$90$		0			0
$91$	4.95358	+	2.15271i	0.519276	+	0.225665i
$92$		0			0
$93$	−2.16621	−	5.84793i	−0.224626	−	0.606402i
$94$		0			0
$95$	0.535310	−	0.309061i	0.0549217	−	0.0317090i
$96$		0			0
$97$		−	6.65337i		−	0.675547i	−0.941227	−	0.337774i	$-0.890326\pi$
$97$		−	6.65337i		−	0.675547i	0.941227	−	0.337774i	$-0.109674\pi$
$98$		0			0
$99$	−7.28165	+	1.36951i	−0.731834	+	0.137641i
$100$		0			0
$101$	−8.06357	−	13.9665i	−0.802355	−	1.38972i	−0.918062	−	0.396437i	$-0.870247\pi$
$101$	−8.06357	−	13.9665i	−0.802355	−	1.38972i	0.115707	−	0.993283i	$-0.463087\pi$
$102$		0			0
$103$	−0.147333	−	0.0850626i	−0.0145171	−	0.00838147i	0.492724	−	0.870186i	$-0.336001\pi$
$103$	−0.147333	−	0.0850626i	−0.0145171	−	0.00838147i	−0.507241	+	0.861804i	$0.669335\pi$
$104$		0			0
$105$	0.594290	−	0.300681i	0.0579967	−	0.0293435i
$106$		0			0
$107$	6.03900	+	3.48662i	0.583813	+	0.337064i	0.762647	−	0.646815i	$-0.223899\pi$
$107$	6.03900	+	3.48662i	0.583813	+	0.337064i	−0.178835	+	0.983879i	$0.557233\pi$
$108$		0			0
$109$	−0.677559	−	1.17357i	−0.0648984	−	0.112407i	0.831751	−	0.555150i	$-0.187339\pi$
$109$	−0.677559	−	1.17357i	−0.0648984	−	0.112407i	−0.896649	+	0.442742i	$0.854006\pi$
$110$		0			0
$111$	7.82532	+	6.49076i	0.742747	+	0.616076i
$112$		0			0
$113$		−	4.00000i		−	0.376288i	−0.982141	−	0.188144i	$-0.939753\pi$
$113$		−	4.00000i		−	0.376288i	0.982141	−	0.188144i	$-0.0602472\pi$
$114$		0			0
$115$	−1.08474	+	0.626273i	−0.101152	+	0.0584002i
$116$		0			0
$117$	2.02905	−	5.77840i	0.187586	−	0.534213i
$118$		0			0
$119$	−4.61817	+	0.527101i	−0.423347	+	0.0483193i
$120$		0			0
$121$	−2.45011	+	4.24371i	−0.222737	+	0.385792i
$122$		0			0
$123$	1.55211	−	9.10490i	0.139949	−	0.820961i
$124$		0			0
$125$	−1.45032			−0.129720
$126$		0			0
$127$	−7.33399			−0.650787			−0.325393	−	0.945579i	$-0.605497\pi$
$127$	−7.33399			−0.650787			−0.325393	+	0.945579i	$0.605497\pi$
$128$		0			0
$129$	−2.67688	+	15.7030i	−0.235687	+	1.38257i
$130$		0			0
$131$	3.04832	−	5.27985i	0.266333	−	0.461303i	−0.701579	−	0.712592i	$-0.747521\pi$
$131$	3.04832	−	5.27985i	0.266333	−	0.461303i	0.967912	+	0.251289i	$0.0808545\pi$
$132$		0			0
$133$	−9.04395	+	6.69494i	−0.784210	+	0.580525i
$134$		0			0
$135$	−0.388702	−	0.647487i	−0.0334542	−	0.0557268i
$136$		0			0
$137$	−17.3832	+	10.0362i	−1.48515	+	0.857451i	−0.999857	−	0.0169018i	$-0.994620\pi$
$137$	−17.3832	+	10.0362i	−1.48515	+	0.857451i	−0.485291	+	0.874353i	$0.661286\pi$
$138$		0			0
$139$			0.117694i			0.00998266i	0.999988	+	0.00499133i	$0.00158880\pi$
$139$			0.117694i			0.00998266i	−0.999988	+	0.00499133i	$0.998411\pi$
$140$		0			0
$141$	12.4032	+	10.2879i	1.04454	+	0.866401i
$142$		0			0
$143$	2.52094	+	4.36639i	0.210811	+	0.365136i
$144$		0			0
$145$	−0.892131	−	0.515072i	−0.0740875	−	0.0427744i
$146$		0			0
$147$	−10.1280	+	6.66513i	−0.835342	+	0.549730i
$148$		0			0
$149$	7.75705	+	4.47853i	0.635482	+	0.366896i	0.782872	−	0.622183i	$-0.213754\pi$
$149$	7.75705	+	4.47853i	0.635482	+	0.366896i	−0.147390	+	0.989078i	$0.547087\pi$
$150$		0			0
$151$	1.37132	+	2.37519i	0.111596	+	0.193290i	0.916414	−	0.400232i	$-0.131070\pi$
$151$	1.37132	+	2.37519i	0.111596	+	0.193290i	−0.804818	+	0.593522i	$0.797737\pi$
$152$		0			0
$153$	0.974184	+	5.17970i	0.0787581	+	0.418754i
$154$		0			0
$155$			0.523291i			0.0420318i
$156$		0			0
$157$	−11.7303	+	6.77249i	−0.936180	+	0.540504i	−0.888761	−	0.458371i	$-0.848433\pi$
$157$	−11.7303	+	6.77249i	−0.936180	+	0.540504i	−0.0474193	+	0.998875i	$0.515100\pi$
$158$		0			0
$159$	−3.12329	−	8.43168i	−0.247693	−	0.668676i
$160$		0			0
$161$	18.3264	−	13.5664i	1.44432	−	1.06918i
$162$		0			0
$163$	2.02428	−	3.50616i	0.158554	−	0.274624i	−0.775793	−	0.630987i	$-0.782650\pi$
$163$	2.02428	−	3.50616i	0.158554	−	0.274624i	0.934347	+	0.356363i	$0.115983\pi$
$164$		0			0
$165$	0.612884	+	0.104478i	0.0477130	+	0.00813361i
$166$		0			0
$167$	3.70521			0.286717			0.143359	−	0.989671i	$-0.454210\pi$
$167$	3.70521			0.286717			0.143359	+	0.989671i	$0.454210\pi$
$168$		0			0
$169$	8.83256			0.679428
$170$		0			0
$171$	8.31193	+	9.68003i	0.635629	+	0.740250i
$172$		0			0
$173$	−11.2370	+	19.4630i	−0.854333	+	1.47975i	0.0229296	+	0.999737i	$0.492701\pi$
$173$	−11.2370	+	19.4630i	−0.854333	+	1.47975i	−0.877263	+	0.480011i	$0.840633\pi$
$174$		0			0
$175$	13.0879	−	1.49381i	0.989352	−	0.112921i
$176$		0			0
$177$	−18.2008	+	6.74198i	−1.36805	+	0.506758i
$178$		0			0
$179$	3.18574	−	1.83929i	0.238113	−	0.137475i	−0.376196	−	0.926540i	$-0.622768\pi$
$179$	3.18574	−	1.83929i	0.238113	−	0.137475i	0.614309	+	0.789065i	$0.289435\pi$
$180$		0			0
$181$			8.01062i			0.595425i	0.954656	+	0.297712i	$0.0962237\pi$
$181$			8.01062i			0.595425i	−0.954656	+	0.297712i	$0.903776\pi$
$182$		0			0
$183$	5.95459	−	7.17892i	0.440176	−	0.530681i
$184$		0			0
$185$	−0.426558	−	0.738821i	−0.0313612	−	0.0543192i
$186$		0			0
$187$	−3.75768	−	2.16950i	−0.274789	−	0.158649i
$188$		0			0
$189$	8.36695	+	10.9084i	0.608606	+	0.793473i
$190$		0			0
$191$	−0.971326	−	0.560795i	−0.0702827	−	0.0405777i	0.464447	−	0.885601i	$-0.346253\pi$
$191$	−0.971326	−	0.560795i	−0.0702827	−	0.0405777i	−0.534730	+	0.845023i	$0.679587\pi$
$192$		0			0
$193$	−9.18421	−	15.9075i	−0.661094	−	1.14505i	−0.980329	−	0.197373i	$-0.936759\pi$
$193$	−9.18421	−	15.9075i	−0.661094	−	1.14505i	0.319235	−	0.947676i	$-0.396574\pi$
$194$		0			0
$195$	−0.328083	+	0.395540i	−0.0234945	+	0.0283252i
$196$		0			0
$197$			0.296699i			0.0211389i	0.999944	+	0.0105695i	$0.00336442\pi$
$197$			0.296699i			0.0211389i	−0.999944	+	0.0105695i	$0.996636\pi$
$198$		0			0
$199$	−23.6874	+	13.6759i	−1.67915	+	0.969460i	−0.716951	+	0.697124i	$0.754463\pi$
$199$	−23.6874	+	13.6759i	−1.67915	+	0.969460i	−0.962202	+	0.272336i	$0.912204\pi$
$200$		0			0
$201$	8.36195	−	3.09746i	0.589807	−	0.218478i
$202$		0			0
$203$	17.1989	+	7.47426i	1.20713	+	0.524590i
$204$		0			0
$205$	−0.387513	+	0.671191i	−0.0270650	+	0.0468780i
$206$		0			0
$207$	−16.8430	−	19.6153i	−1.17067	−	1.36336i
$208$		0			0
$209$	−10.5039			−0.726571
$210$		0			0
$211$	21.0295			1.44773			0.723864	−	0.689942i	$-0.242364\pi$
$211$	21.0295			1.44773			0.723864	+	0.689942i	$0.242364\pi$
$212$		0			0
$213$	−13.3063	−	2.26832i	−0.911734	−	0.155423i
$214$		0			0
$215$	0.668333	−	1.15759i	0.0455800	−	0.0789468i
$216$		0			0
$217$	−1.08025	−	9.46457i	−0.0733323	−	0.642497i
$218$		0			0
$219$	−7.85121	−	21.1952i	−0.530535	−	1.43224i
$220$		0			0
$221$	3.10597	−	1.79323i	0.208930	−	0.120626i
$222$		0			0
$223$			6.89447i			0.461688i	0.972991	+	0.230844i	$0.0741487\pi$
$223$			6.89447i			0.461688i	−0.972991	+	0.230844i	$0.925851\pi$
$224$		0			0
$225$	−2.76084	−	14.6793i	−0.184056	−	0.978617i
$226$		0			0
$227$	6.70734	+	11.6174i	0.445182	+	0.771077i	0.998065	−	0.0621816i	$-0.0198058\pi$
$227$	6.70734	+	11.6174i	0.445182	+	0.771077i	−0.552883	+	0.833259i	$0.686472\pi$
$228$		0			0
$229$	−5.51012	−	3.18127i	−0.364119	−	0.210224i	0.306767	−	0.951785i	$-0.400753\pi$
$229$	−5.51012	−	3.18127i	−0.364119	−	0.210224i	−0.670886	+	0.741560i	$0.734086\pi$
$230$		0			0
$231$	−11.3007	−	0.624454i	−0.743530	−	0.0410861i
$232$		0			0
$233$	4.29295	+	2.47853i	0.281240	+	0.162374i	0.633985	−	0.773346i	$-0.281418\pi$
$233$	4.29295	+	2.47853i	0.281240	+	0.162374i	−0.352744	+	0.935720i	$0.614752\pi$
$234$		0			0
$235$	−0.676100	−	1.17104i	−0.0441039	−	0.0763903i
$236$		0			0
$237$	−7.62755	−	6.32672i	−0.495463	−	0.410964i
$238$		0			0
$239$		−	17.3756i		−	1.12394i	−0.827159	−	0.561968i	$-0.810044\pi$
$239$		−	17.3756i		−	1.12394i	0.827159	−	0.561968i	$-0.189956\pi$
$240$		0			0
$241$	12.5626	−	7.25302i	0.809228	−	0.467208i	−0.0374597	−	0.999298i	$-0.511927\pi$
$241$	12.5626	−	7.25302i	0.809228	−	0.467208i	0.846688	+	0.532090i	$0.178593\pi$
$242$		0			0
$243$	11.6518	−	10.3555i	0.747462	−	0.664305i
$244$		0			0
$245$	0.991204	−	0.229251i	0.0633257	−	0.0146463i
$246$		0			0
$247$	4.34109	−	7.51899i	0.276217	−	0.478422i
$248$		0			0
$249$	−4.65171	+	27.2876i	−0.294790	+	1.72928i
$250$		0			0
$251$	−3.49783			−0.220781			−0.110391	−	0.993888i	$-0.535210\pi$
$251$	−3.49783			−0.220781			−0.110391	+	0.993888i	$0.535210\pi$
$252$		0			0
$253$	21.2848			1.33816
$254$		0			0
$255$	0.0743190	−	0.435966i	0.00465404	−	0.0273013i
$256$		0			0
$257$	7.96781	−	13.8006i	0.497018	−	0.860861i	−0.502976	−	0.864300i	$-0.667762\pi$
$257$	7.96781	−	13.8006i	0.497018	−	0.860861i	0.999994	+	0.00343985i	$0.00109494\pi$
$258$		0			0
$259$	9.24018	+	12.4822i	0.574157	+	0.775607i
$260$		0			0
$261$	7.04490	−	20.0627i	0.436069	−	1.24185i
$262$		0			0
$263$	−12.4343	+	7.17892i	−0.766729	+	0.442671i	−0.831706	−	0.555216i	$-0.812636\pi$
$263$	−12.4343	+	7.17892i	−0.766729	+	0.442671i	0.0649777	+	0.997887i	$0.479302\pi$
$264$		0			0
$265$			0.754493i			0.0463482i
$266$		0			0
$267$	11.5784	+	9.60373i	0.708584	+	0.587739i
$268$		0			0
$269$	3.68211	+	6.37760i	0.224502	+	0.388849i	0.956170	−	0.292812i	$-0.0945911\pi$
$269$	3.68211	+	6.37760i	0.224502	+	0.388849i	−0.731668	+	0.681661i	$0.761258\pi$
$270$		0			0
$271$	10.8537	+	6.26636i	0.659313	+	0.380654i	0.792015	−	0.610501i	$-0.209032\pi$
$271$	10.8537	+	6.26636i	0.659313	+	0.380654i	−0.132702	+	0.991156i	$0.542365\pi$
$272$		0			0
$273$	5.11738	−	7.83126i	0.309718	−	0.473969i
$274$		0			0
$275$	10.6493	+	6.14835i	0.642174	+	0.370759i
$276$		0			0
$277$	−16.2409	−	28.1300i	−0.975819	−	1.69017i	−0.677205	−	0.735794i	$-0.736809\pi$
$277$	−16.2409	−	28.1300i	−0.975819	−	1.69017i	−0.298614	−	0.954374i	$-0.596524\pi$
$278$		0			0
$279$	−10.6154	+	1.99651i	−0.635526	+	0.119528i
$280$		0			0
$281$		−	10.1758i		−	0.607037i	−0.952826	−	0.303518i	$-0.901839\pi$
$281$		−	10.1758i		−	0.607037i	0.952826	−	0.303518i	$-0.0981614\pi$
$282$		0			0
$283$	−1.18666	+	0.685120i	−0.0705397	+	0.0407261i	−0.534855	−	0.844944i	$-0.679634\pi$
$283$	−1.18666	+	0.685120i	−0.0705397	+	0.0407261i	0.464315	+	0.885670i	$0.346300\pi$
$284$		0			0
$285$	−0.371889	−	1.00396i	−0.0220288	−	0.0594692i
$286$		0			0
$287$	5.62323	−	12.9395i	0.331929	−	0.763797i
$288$		0			0
$289$	6.95676	−	12.0495i	0.409221	−	0.708792i
$290$		0			0
$291$	−11.3601	−	1.93655i	−0.665941	−	0.113523i
$292$		0			0
$293$	16.9961			0.992923			0.496461	−	0.868059i	$-0.334632\pi$
$293$	16.9961			0.992923			0.496461	+	0.868059i	$0.334632\pi$
$294$		0			0
$295$	1.62866			0.0948243
$296$		0			0
$297$	0.218914	+	12.8315i	0.0127027	+	0.744556i
$298$		0			0
$299$	−8.79665	+	15.2362i	−0.508723	+	0.881135i
$300$		0			0
$301$	−9.69824	+	22.3165i	−0.558997	+	1.28630i
$302$		0			0
$303$	−26.1937	+	9.70276i	−1.50479	+	0.557409i
$304$		0			0
$305$	−0.677791	+	0.391323i	−0.0388102	+	0.0224071i
$306$		0			0
$307$		−	20.9023i		−	1.19296i	−0.802629	−	0.596479i	$-0.796566\pi$
$307$		−	20.9023i		−	1.19296i	0.802629	−	0.596479i	$-0.203434\pi$
$308$		0			0
$309$	−0.188121	+	0.226800i	−0.0107018	+	0.0129022i
$310$		0			0
$311$	−5.74040	−	9.94267i	−0.325508	−	0.563797i	0.656107	−	0.754668i	$-0.272202\pi$
$311$	−5.74040	−	9.94267i	−0.325508	−	0.563797i	−0.981615	+	0.190871i	$0.938869\pi$
$312$		0			0
$313$	8.57172	+	4.94889i	0.484502	+	0.279728i	0.722291	−	0.691589i	$-0.243089\pi$
$313$	8.57172	+	4.94889i	0.484502	+	0.279728i	−0.237788	+	0.971317i	$0.576423\pi$
$314$		0			0
$315$	−0.340413	−	1.10222i	−0.0191801	−	0.0621030i
$316$		0			0
$317$	5.74547	+	3.31715i	0.322698	+	0.186310i	0.652594	−	0.757707i	$-0.273681\pi$
$317$	5.74547	+	3.31715i	0.322698	+	0.186310i	−0.329897	+	0.944017i	$0.607014\pi$
$318$		0			0
$319$	8.75275	+	15.1602i	0.490060	+	0.848809i
$320$		0			0
$321$	7.71086	−	9.29629i	0.430378	−	0.518868i
$322$		0			0
$323$			7.47181i			0.415742i
$324$		0			0
$325$	−8.80231	+	5.08202i	−0.488264	+	0.281900i
$326$		0			0
$327$	−2.20098	+	0.815296i	−0.121715	+	0.0450860i
$328$		0			0
$329$	14.6458	+	19.7845i	0.807449	+	1.09075i
$330$		0			0
$331$	−7.36537	+	12.7572i	−0.404837	+	0.701199i	−0.994303	−	0.106595i	$-0.966005\pi$
$331$	−7.36537	+	12.7572i	−0.404837	+	0.701199i	0.589465	+	0.807794i	$0.299339\pi$
$332$		0			0
$333$	13.3601	−	11.4719i	0.732130	−	0.628656i
$334$		0			0
$335$	−0.748254			−0.0408815
$336$		0			0
$337$	−30.7209			−1.67347			−0.836737	−	0.547605i	$-0.815540\pi$
$337$	−30.7209			−1.67347			−0.836737	+	0.547605i	$0.815540\pi$
$338$		0			0
$339$	−6.82968	−	1.16425i	−0.370937	−	0.0632335i
$340$		0			0
$341$	4.44621	−	7.70106i	0.240776	−	0.417036i
$342$		0			0
$343$	−17.4543	+	6.19257i	−0.942443	+	0.334367i
$344$		0			0
$345$	0.753584	+	2.03439i	0.0405716	+	0.109528i
$346$		0			0
$347$	−14.5124	+	8.37875i	−0.779068	+	0.449795i	−0.836100	−	0.548577i	$-0.815170\pi$
$347$	−14.5124	+	8.37875i	−0.779068	+	0.449795i	0.0570320	+	0.998372i	$0.481836\pi$
$348$		0			0
$349$		−	3.12385i		−	0.167216i	−0.996499	−	0.0836080i	$-0.973356\pi$
$349$		−	3.12385i		−	0.167216i	0.996499	−	0.0836080i	$-0.0266443\pi$
$350$		0			0
$351$	−9.27558	−	5.14632i	−0.495094	−	0.274690i
$352$		0			0
$353$	17.7450	+	30.7353i	0.944473	+	1.63587i	0.756804	+	0.653642i	$0.226760\pi$
$353$	17.7450	+	30.7353i	0.944473	+	1.63587i	0.187669	+	0.982232i	$0.439907\pi$
$354$		0			0
$355$	0.980910	+	0.566328i	0.0520613	+	0.0300576i
$356$		0			0
$357$	−0.444197	+	8.03858i	−0.0235094	+	0.425447i
$358$		0			0
$359$	−5.42817	−	3.13395i	−0.286488	−	0.165404i	0.349869	−	0.936799i	$-0.386226\pi$
$359$	−5.42817	−	3.13395i	−0.286488	−	0.165404i	−0.636357	+	0.771395i	$0.719559\pi$
$360$		0			0
$361$	−0.456052	−	0.789905i	−0.0240027	−	0.0415739i
$362$		0			0
$363$	6.53266	+	5.41855i	0.342876	+	0.284400i
$364$		0			0
$365$			1.89662i			0.0992734i
$366$		0			0
$367$	−14.5823	+	8.41907i	−0.761188	+	0.439472i	−0.829722	−	0.558177i	$-0.811501\pi$
$367$	−14.5823	+	8.41907i	−0.761188	+	0.439472i	0.0685342	+	0.997649i	$0.478168\pi$
$368$		0			0
$369$	−15.0941	−	5.30020i	−0.785769	−	0.275918i
$370$		0			0
$371$	−1.55753	−	13.6462i	−0.0808631	−	0.708478i
$372$		0			0
$373$	0.617106	−	1.06886i	0.0319526	−	0.0553435i	−0.849607	−	0.527416i	$-0.823161\pi$
$373$	0.617106	−	1.06886i	0.0319526	−	0.0553435i	0.881559	+	0.472073i	$0.156494\pi$
$374$		0			0
$375$	−0.422134	+	2.47630i	−0.0217989	+	0.127875i
$376$		0			0
$377$	−14.4695			−0.745215
$378$		0			0
$379$	−14.3895			−0.739141			−0.369571	−	0.929203i	$-0.620495\pi$
$379$	−14.3895			−0.739141			−0.369571	+	0.929203i	$0.620495\pi$
$380$		0			0
$381$	−2.13466	+	12.5222i	−0.109362	+	0.641532i
$382$		0			0
$383$	−4.95842	+	8.58824i	−0.253364	+	0.438839i	−0.964450	−	0.264266i	$-0.914870\pi$
$383$	−4.95842	+	8.58824i	−0.253364	+	0.438839i	0.711086	+	0.703105i	$0.248204\pi$
$384$		0			0
$385$	0.871008	+	0.378520i	0.0443907	+	0.0192912i
$386$		0			0
$387$	26.0325	+	9.14113i	1.32330	+	0.464670i
$388$		0			0
$389$	11.5061	−	6.64306i	0.583383	−	0.336816i	−0.179094	−	0.983832i	$-0.557317\pi$
$389$	11.5061	−	6.64306i	0.583383	−	0.336816i	0.762477	+	0.647016i	$0.223983\pi$
$390$		0			0
$391$		−	15.1406i		−	0.765695i
$392$		0			0
$393$	−8.12767	−	6.74154i	−0.409987	−	0.340066i
$394$		0			0
$395$	0.415778	+	0.720148i	0.0209201	+	0.0362346i
$396$		0			0
$397$	21.0410	+	12.1480i	1.05602	+	0.609693i	0.924328	−	0.381598i	$-0.124626\pi$
$397$	21.0410	+	12.1480i	1.05602	+	0.609693i	0.131691	+	0.991291i	$0.457959\pi$
$398$		0			0
$399$	8.79872	+	17.3905i	0.440487	+	0.870612i
$400$		0			0
$401$	−12.4125	−	7.16635i	−0.619850	−	0.357870i	0.156961	−	0.987605i	$-0.449830\pi$
$401$	−12.4125	−	7.16635i	−0.619850	−	0.357870i	−0.776810	+	0.629735i	$0.783164\pi$
$402$		0			0
$403$	3.67508	+	6.36543i	0.183069	+	0.317085i
$404$		0			0
$405$	−1.21867	+	0.475218i	−0.0605562	+	0.0236138i
$406$		0			0
$407$			14.4972i			0.718600i
$408$		0			0
$409$	17.3256	−	10.0029i	0.856695	−	0.494613i	−0.00620937	−	0.999981i	$-0.501977\pi$
$409$	17.3256	−	10.0029i	0.856695	−	0.494613i	0.862904	+	0.505368i	$0.168643\pi$
$410$		0			0
$411$	12.0764	+	32.6016i	0.595685	+	1.60812i
$412$		0			0
$413$	−29.4570	+	3.36211i	−1.44948	+	0.165439i
$414$		0			0
$415$	1.16139	−	2.01158i	0.0570102	−	0.0987446i
$416$		0			0
$417$	0.200953	+	0.0342563i	0.00984070	+	0.00167754i
$418$		0			0
$419$	27.7445			1.35541			0.677704	−	0.735335i	$-0.262975\pi$
$419$	27.7445			1.35541			0.677704	+	0.735335i	$0.262975\pi$
$420$		0			0
$421$	−1.53586			−0.0748533			−0.0374267	−	0.999299i	$-0.511916\pi$
$421$	−1.53586			−0.0748533			−0.0374267	+	0.999299i	$0.511916\pi$
$422$		0			0
$423$	21.1760	−	18.1831i	1.02961	−	0.884093i
$424$		0			0
$425$	4.37354	−	7.57519i	0.212148	−	0.367451i
$426$		0			0
$427$	11.4511	−	8.47690i	0.554159	−	0.410226i
$428$		0			0
$429$	8.18901	−	3.03340i	0.395369	−	0.146454i
$430$		0			0
$431$	14.8277	−	8.56080i	0.714227	−	0.412359i	−0.0983974	−	0.995147i	$-0.531372\pi$
$431$	14.8277	−	8.56080i	0.714227	−	0.412359i	0.812624	+	0.582788i	$0.198038\pi$
$432$		0			0
$433$			27.5219i			1.32262i	0.750113	+	0.661310i	$0.229999\pi$
$433$			27.5219i			1.32262i	−0.750113	+	0.661310i	$0.770001\pi$
$434$		0			0
$435$	−1.13911	+	1.37332i	−0.0546162	+	0.0658459i
$436$		0			0
$437$	−18.3264	−	31.7422i	−0.876670	−	1.51844i
$438$		0			0
$439$	−18.9922	−	10.9651i	−0.906446	−	0.523337i	−0.0271602	−	0.999631i	$-0.508646\pi$
$439$	−18.9922	−	10.9651i	−0.906446	−	0.523337i	−0.879286	+	0.476294i	$0.841980\pi$
$440$		0			0
$441$	8.43228	+	19.2327i	0.401537	+	0.915843i
$442$		0			0
$443$	−17.7589	−	10.2531i	−0.843750	−	0.487139i	0.0147873	−	0.999891i	$-0.495293\pi$
$443$	−17.7589	−	10.2531i	−0.843750	−	0.487139i	−0.858537	+	0.512752i	$0.828626\pi$
$444$		0			0
$445$	−0.631136	−	1.09316i	−0.0299187	−	0.0518207i
$446$		0			0
$447$	9.90453	−	11.9410i	0.468468	−	0.564790i
$448$		0			0
$449$		−	18.7692i		−	0.885773i	−0.896578	−	0.442886i	$-0.853954\pi$
$449$		−	18.7692i		−	0.885773i	0.896578	−	0.442886i	$-0.146046\pi$
$450$		0			0
$451$	11.4057	−	6.58509i	0.537074	−	0.310080i
$452$		0			0
$453$	4.45458	−	1.65008i	0.209295	−	0.0775276i
$454$		0			0
$455$	−0.630928	+	0.467055i	−0.0295783	+	0.0218959i
$456$		0			0
$457$	−3.79670	+	6.57607i	−0.177602	+	0.307616i	−0.941059	−	0.338243i	$-0.890167\pi$
$457$	−3.79670	+	6.57607i	−0.177602	+	0.307616i	0.763457	+	0.645859i	$0.223501\pi$
$458$		0			0
$459$	9.12747	−	0.155721i	0.426034	−	0.00726845i
$460$		0			0
$461$	−29.2727			−1.36337			−0.681683	−	0.731648i	$-0.738752\pi$
$461$	−29.2727			−1.36337			−0.681683	+	0.731648i	$0.738752\pi$
$462$		0			0
$463$	11.8326			0.549906			0.274953	−	0.961458i	$-0.411338\pi$
$463$	11.8326			0.549906			0.274953	+	0.961458i	$0.411338\pi$
$464$		0			0
$465$	0.893478	+	0.152311i	0.0414340	+	0.00706325i
$466$		0			0
$467$	2.58282	−	4.47358i	0.119519	−	0.207013i	−0.800058	−	0.599922i	$-0.795198\pi$
$467$	2.58282	−	4.47358i	0.119519	−	0.207013i	0.919577	+	0.392910i	$0.128531\pi$
$468$		0			0
$469$	13.5334	−	1.54465i	0.624914	−	0.0713254i
$470$		0			0
$471$	8.14923	+	21.9998i	0.375497	+	1.01370i
$472$		0			0
$473$	−19.6712	+	11.3572i	−0.904481	+	0.522202i
$474$		0			0
$475$		−	21.1751i		−	0.971580i
$476$		0			0
$477$	−15.3055	+	2.87862i	−0.700790	+	0.131803i
$478$		0			0
$479$	−9.85496	−	17.0693i	−0.450284	−	0.779915i	0.548119	−	0.836400i	$-0.315344\pi$
$479$	−9.85496	−	17.0693i	−0.450284	−	0.779915i	−0.998403	+	0.0564848i	$0.982011\pi$
$480$		0			0
$481$	−10.3775	−	5.99145i	−0.473173	−	0.273187i
$482$		0			0
$483$	−17.8295	−	35.2395i	−0.811268	−	1.60345i
$484$		0			0
$485$	0.837439	+	0.483496i	0.0380261	+	0.0219544i
$486$		0			0
$487$	2.50360	+	4.33637i	0.113449	+	0.196500i	0.917159	−	0.398522i	$-0.130477\pi$
$487$	2.50360	+	4.33637i	0.113449	+	0.196500i	−0.803710	+	0.595022i	$0.797143\pi$
$488$		0			0
$489$	−5.39730	−	4.47682i	−0.244074	−	0.202449i
$490$		0			0
$491$		−	3.55902i		−	0.160616i	−0.996770	−	0.0803081i	$-0.974410\pi$
$491$		−	3.55902i		−	0.160616i	0.996770	−	0.0803081i	$-0.0255904\pi$
$492$		0			0
$493$	10.7840	−	6.22614i	0.485687	−	0.280411i
$494$		0			0
$495$	0.356776	−	1.01604i	0.0160359	−	0.0456676i
$496$		0			0
$497$	−18.9104	−	8.21804i	−0.848249	−	0.368629i
$498$		0			0
$499$	0.404702	−	0.700965i	0.0181170	−	0.0313795i	−0.856825	−	0.515608i	$-0.827566\pi$
$499$	0.404702	−	0.700965i	0.0181170	−	0.0313795i	0.874942	+	0.484228i	$0.160900\pi$
$500$		0			0
$501$	1.07845	−	6.32634i	0.0481815	−	0.282640i
$502$		0			0
$503$	−9.47070			−0.422278			−0.211139	−	0.977456i	$-0.567717\pi$
$503$	−9.47070			−0.422278			−0.211139	+	0.977456i	$0.567717\pi$
$504$		0			0
$505$	2.34390			0.104302
$506$		0			0
$507$	2.57083	−	15.0809i	0.114175	−	0.669766i
$508$		0			0
$509$	5.24404	−	9.08294i	0.232438	−	0.402594i	−0.726087	−	0.687603i	$-0.758663\pi$
$509$	5.24404	−	9.08294i	0.232438	−	0.402594i	0.958525	+	0.285009i	$0.0919965\pi$
$510$		0			0
$511$	−3.91526	−	34.3034i	−0.173201	−	1.51749i
$512$		0			0
$513$	18.9472	−	11.3744i	0.836538	−	0.502194i
$514$		0			0
$515$	0.0214131	−	0.0123629i	0.000943576	−	0.000544774i
$516$		0			0
$517$			22.9783i			1.01058i
$518$		0			0
$519$	29.9609	+	24.8512i	1.31514	+	1.09085i
$520$		0			0
$521$	4.77854	+	8.27667i	0.209351	+	0.362607i	0.951510	−	0.307617i	$-0.0995314\pi$
$521$	4.77854	+	8.27667i	0.209351	+	0.362607i	−0.742159	+	0.670224i	$0.766198\pi$
$522$		0			0
$523$	−24.0305	−	13.8740i	−1.05078	−	0.606668i	−0.127912	−	0.991785i	$-0.540828\pi$
$523$	−24.0305	−	13.8740i	−1.05078	−	0.606668i	−0.922868	+	0.385117i	$0.874161\pi$
$524$		0			0
$525$	1.25885	−	22.7813i	0.0549408	−	0.994259i
$526$		0			0
$527$	−5.47804	−	3.16275i	−0.238627	−	0.137771i
$528$		0			0
$529$	25.6360	+	44.4029i	1.11461	+	1.93056i
$530$		0			0
$531$	6.21383	+	33.0387i	0.269657	+	1.43376i
$532$		0			0
$533$			10.8860i			0.471526i
$534$		0			0
$535$	−0.877700	+	0.506740i	−0.0379463	+	0.0219083i
$536$		0			0
$537$	−2.21318	−	5.97474i	−0.0955060	−	0.257829i
$538$		0			0
$539$	−16.5350	−	5.04809i	−0.712213	−	0.217437i
$540$		0			0
$541$	0.577777	−	1.00074i	0.0248406	−	0.0430251i	−0.853338	−	0.521358i	$-0.825426\pi$
$541$	0.577777	−	1.00074i	0.0248406	−	0.0430251i	0.878178	+	0.478333i	$0.158759\pi$
$542$		0			0
$543$	13.6775	+	2.33160i	0.586958	+	0.100058i
$544$		0			0
$545$	0.196951			0.00843645
$546$		0			0
$547$	16.1394			0.690070			0.345035	−	0.938590i	$-0.387867\pi$
$547$	16.1394			0.690070			0.345035	+	0.938590i	$0.387867\pi$
$548$		0			0
$549$	−10.5243	−	12.2565i	−0.449165	−	0.523095i
$550$		0			0
$551$	15.0724	−	26.1061i	0.642104	−	1.11216i
$552$		0			0
$553$	−9.00665	−	12.1667i	−0.383002	−	0.517383i
$554$		0			0
$555$	−1.38563	+	0.513271i	−0.0588168	+	0.0217871i
$556$		0			0
$557$	32.1074	−	18.5372i	1.36043	−	0.785447i	0.370753	−	0.928732i	$-0.379100\pi$
$557$	32.1074	−	18.5372i	1.36043	−	0.785447i	0.989682	+	0.143284i	$0.0457663\pi$
$558$		0			0
$559$		−	18.7749i		−	0.794092i
$560$		0			0
$561$	−4.79796	+	5.78447i	−0.202570	+	0.244221i
$562$		0			0
$563$	−7.79584	−	13.5028i	−0.328556	−	0.569075i	0.653670	−	0.756780i	$-0.273228\pi$
$563$	−7.79584	−	13.5028i	−0.328556	−	0.569075i	−0.982225	+	0.187705i	$0.939895\pi$
$564$		0			0
$565$	0.503468	+	0.290677i	0.0211810	+	0.0122289i
$566$		0			0
$567$	21.0606	−	11.1108i	0.884462	−	0.466612i
$568$		0			0
$569$	−13.0276	−	7.52147i	−0.546144	−	0.315316i	0.201421	−	0.979505i	$-0.435444\pi$
$569$	−13.0276	−	7.52147i	−0.546144	−	0.315316i	−0.747565	+	0.664188i	$0.768777\pi$
$570$		0			0
$571$	−2.81334	−	4.87284i	−0.117735	−	0.203922i	0.801135	−	0.598484i	$-0.204230\pi$
$571$	−2.81334	−	4.87284i	−0.117735	−	0.203922i	−0.918870	+	0.394561i	$0.870897\pi$
$572$		0			0
$573$	−1.24023	+	1.49523i	−0.0518114	+	0.0624643i
$574$		0			0
$575$			42.9086i			1.78941i
$576$		0			0
$577$	19.2278	−	11.1012i	0.800465	−	0.462149i	−0.0431688	−	0.999068i	$-0.513745\pi$
$577$	19.2278	−	11.1012i	0.800465	−	0.462149i	0.843634	+	0.536919i	$0.180412\pi$
$578$		0			0
$579$	−29.8340	+	11.0512i	−1.23986	+	0.459273i
$580$		0			0
$581$	−16.8530	+	38.7802i	−0.699179	+	1.60887i
$582$		0			0
$583$	6.41064	−	11.1036i	0.265502	−	0.459863i
$584$		0			0
$585$	0.579860	+	0.675302i	0.0239743	+	0.0279203i
$586$		0			0
$587$	20.9245			0.863648			0.431824	−	0.901958i	$-0.357870\pi$
$587$	20.9245			0.863648			0.431824	+	0.901958i	$0.357870\pi$
$588$		0			0
$589$	−15.3129			−0.630956
$590$		0			0
$591$	0.506589	+	0.0863581i	0.0208383	+	0.00355230i
$592$		0			0
$593$	−10.5845	+	18.3329i	−0.434654	+	0.752842i	−0.997267	−	0.0738778i	$-0.976463\pi$
$593$	−10.5845	+	18.3329i	−0.434654	+	0.752842i	0.562614	+	0.826720i	$0.309796\pi$
$594$		0			0
$595$	0.269255	−	0.619579i	0.0110384	−	0.0254003i
$596$		0			0
$597$	16.4560	+	44.4248i	0.673499	+	1.81819i
$598$		0			0
$599$	−4.58648	+	2.64801i	−0.187399	+	0.108195i	−0.590764	−	0.806844i	$-0.701174\pi$
$599$	−4.58648	+	2.64801i	−0.187399	+	0.108195i	0.403366	+	0.915039i	$0.367840\pi$
$600$		0			0
$601$			37.5346i			1.53107i	0.643396	+	0.765533i	$0.277525\pi$
$601$			37.5346i			1.53107i	−0.643396	+	0.765533i	$0.722475\pi$
$602$		0			0
$603$	−2.85481	−	15.1789i	−0.116257	−	0.618133i
$604$		0			0
$605$	−0.356095	−	0.616775i	−0.0144773	−	0.0250755i
$606$		0			0
$607$	34.2123	+	19.7525i	1.38864	+	0.801729i	0.993162	−	0.116748i	$-0.0372469\pi$
$607$	34.2123	+	19.7525i	1.38864	+	0.801729i	0.395474	+	0.918477i	$0.370580\pi$
$608$		0			0
$609$	17.7677	−	27.1903i	0.719982	−	1.10181i
$610$		0			0
$611$	−16.4485	−	9.49653i	−0.665434	−	0.384189i
$612$		0			0
$613$	−7.19736	−	12.4662i	−0.290699	−	0.503505i	0.683277	−	0.730160i	$-0.260554\pi$
$613$	−7.19736	−	12.4662i	−0.290699	−	0.503505i	−0.973975	+	0.226655i	$0.927221\pi$
$614$		0			0
$615$	1.03321	+	0.857006i	0.0416632	+	0.0345578i
$616$		0			0
$617$		−	12.1573i		−	0.489435i	−0.969594	−	0.244718i	$-0.921305\pi$
$617$		−	12.1573i		−	0.489435i	0.969594	−	0.244718i	$-0.0786952\pi$
$618$		0			0
$619$	−16.8732	+	9.74173i	−0.678190	+	0.391553i	−0.799173	−	0.601101i	$-0.794729\pi$
$619$	−16.8732	+	9.74173i	−0.678190	+	0.391553i	0.120983	+	0.992655i	$0.461395\pi$
$620$		0			0
$621$	−38.3940	+	23.0488i	−1.54070	+	0.924918i
$622$		0			0
$623$	13.6718	+	18.4687i	0.547748	+	0.739932i
$624$		0			0
$625$	−12.3418	+	21.3766i	−0.493672	+	0.855065i
$626$		0			0
$627$	−3.05730	+	17.9346i	−0.122097	+	0.716239i
$628$		0			0
$629$	10.3124			0.411182
$630$		0			0
$631$	−31.3846			−1.24940			−0.624701	−	0.780864i	$-0.714779\pi$
$631$	−31.3846			−1.24940			−0.624701	+	0.780864i	$0.714779\pi$
$632$		0			0
$633$	6.12091	−	35.9061i	0.243284	−	1.42714i
$634$		0			0
$635$	0.532956	−	0.923107i	0.0211497	−	0.0366324i
$636$		0			0
$637$	10.4472	−	9.74991i	0.413933	−	0.386305i
$638$		0			0
$639$	−7.74596	+	22.0592i	−0.306425	+	0.872650i
$640$		0			0
$641$	36.0118	−	20.7914i	1.42238	−	0.821211i	0.425878	−	0.904781i	$-0.359965\pi$
$641$	36.0118	−	20.7914i	1.42238	−	0.821211i	0.996502	+	0.0835697i	$0.0266321\pi$
$642$		0			0
$643$			13.5290i			0.533531i	0.963761	+	0.266766i	$0.0859549\pi$
$643$			13.5290i			0.533531i	−0.963761	+	0.266766i	$0.914045\pi$
$644$		0			0
$645$	−1.78196	−	1.47806i	−0.0701646	−	0.0581984i
$646$		0			0
$647$	15.0442	+	26.0573i	0.591449	+	1.02442i	0.994038	+	0.109038i	$0.0347771\pi$
$647$	15.0442	+	26.0573i	0.591449	+	1.02442i	−0.402589	+	0.915381i	$0.631890\pi$
$648$		0			0
$649$	−23.9683	−	13.8381i	−0.940839	−	0.543193i
$650$		0			0
$651$	−16.4744	−	0.910345i	−0.645684	−	0.0356793i
$652$		0			0
$653$	18.3717	+	10.6069i	0.718941	+	0.415081i	0.814363	−	0.580356i	$-0.197087\pi$
$653$	18.3717	+	10.6069i	0.718941	+	0.415081i	−0.0954221	+	0.995437i	$0.530420\pi$
$654$		0			0
$655$	0.443039	+	0.767366i	0.0173110	+	0.0299835i
$656$		0			0
$657$	−38.4743	+	7.23615i	−1.50103	+	0.282309i
$658$		0			0
$659$			2.67926i			0.104369i	0.998637	+	0.0521846i	$0.0166184\pi$
$659$			2.67926i			0.104369i	−0.998637	+	0.0521846i	$0.983382\pi$
$660$		0			0
$661$	4.79785	−	2.77004i	0.186615	−	0.107742i	−0.403782	−	0.914855i	$-0.632305\pi$
$661$	4.79785	−	2.77004i	0.186615	−	0.107742i	0.590397	+	0.807113i	$0.298971\pi$
$662$		0			0
$663$	−2.15777	−	5.82513i	−0.0838007	−	0.226229i
$664$		0			0
$665$	−0.185455	−	1.62485i	−0.00719162	−	0.0630090i
$666$		0			0
$667$	−30.5422	+	52.9006i	−1.18260	+	2.04832i
$668$		0			0
$669$	11.7718	+	2.00673i	0.455123	+	0.0775846i
$670$		0			0
$671$	13.2997			0.513429
$672$		0			0
$673$	−17.1946			−0.662804			−0.331402	−	0.943490i	$-0.607522\pi$
$673$	−17.1946			−0.662804			−0.331402	+	0.943490i	$0.607522\pi$
$674$		0			0
$675$	−25.8672	+	0.441314i	−0.995630	+	0.0169862i
$676$		0			0
$677$	7.23319	−	12.5283i	0.277994	−	0.481500i	−0.692892	−	0.721041i	$-0.743664\pi$
$677$	7.23319	−	12.5283i	0.277994	−	0.481500i	0.970886	+	0.239541i	$0.0769971\pi$
$678$		0			0
$679$	−16.1446	−	7.01605i	−0.619571	−	0.269251i
$680$		0			0
$681$	21.7881	−	8.07083i	0.834923	−	0.309275i
$682$		0			0
$683$	28.1356	−	16.2441i	1.07658	−	0.621564i	0.146609	−	0.989195i	$-0.453164\pi$
$683$	28.1356	−	16.2441i	1.07658	−	0.621564i	0.929972	+	0.367630i	$0.119831\pi$
$684$		0			0
$685$		−	2.91730i		−	0.111464i
$686$		0			0
$687$	−7.03555	+	8.48214i	−0.268423	+	0.323614i
$688$		0			0
$689$	5.29882	+	9.17783i	0.201869	+	0.349647i
$690$		0			0
$691$	−28.0961	−	16.2213i	−1.06883	−	0.617087i	−0.140966	−	0.990014i	$-0.545021\pi$
$691$	−28.0961	−	16.2213i	−1.06883	−	0.617087i	−0.927861	+	0.372927i	$0.878354\pi$
$692$		0			0
$693$	−4.35542	+	19.1133i	−0.165449	+	0.726053i
$694$		0			0
$695$	−0.0148138	−	0.00855273i	−0.000561918	−	0.000324423i
$696$		0			0
$697$	−4.68421	−	8.11329i	−0.177427	−	0.307313i
$698$		0			0
$699$	5.48142	−	6.60845i	0.207326	−	0.249955i
$700$		0			0
$701$			30.3777i			1.14735i	0.819084	+	0.573674i	$0.194482\pi$
$701$			30.3777i			1.14735i	−0.819084	+	0.573674i	$0.805518\pi$
$702$		0			0
$703$	21.6198	−	12.4822i	0.815407	−	0.470776i
$704$		0			0
$705$	−2.19625	+	0.813541i	−0.0827154	+	0.0306397i
$706$		0			0
$707$	−42.3932	+	4.83860i	−1.59436	+	0.181974i
$708$		0			0
$709$	16.2569	−	28.1578i	0.610542	−	1.05749i	−0.380607	−	0.924737i	$-0.624285\pi$
$709$	16.2569	−	28.1578i	0.610542	−	1.05749i	0.991149	−	0.132753i	$-0.0423816\pi$
$710$		0			0
$711$	−13.0225	+	11.1820i	−0.488380	+	0.419356i
$712$		0			0
$713$	31.0295			1.16207
$714$		0			0
$715$	−0.732778			−0.0274044
$716$		0			0
$717$	−29.6675	−	5.05741i	−1.10795	−	0.188872i
$718$		0			0
$719$	−5.29867	+	9.17757i	−0.197607	+	0.342266i	−0.947752	−	0.319008i	$-0.896650\pi$
$719$	−5.29867	+	9.17757i	−0.197607	+	0.342266i	0.750145	+	0.661273i	$0.229984\pi$
$720$		0			0
$721$	−0.361770	+	0.267807i	−0.0134730	+	0.00997365i
$722$		0			0
$723$	−8.72744	−	23.5607i	−0.324577	−	0.876232i
$724$		0			0
$725$	−30.5618	+	17.6449i	−1.13504	+	0.655314i
$726$		0			0
$727$			31.3600i			1.16308i	0.813518	+	0.581540i	$0.197549\pi$
$727$			31.3600i			1.16308i	−0.813518	+	0.581540i	$0.802451\pi$
$728$		0			0
$729$	−14.2898	−	22.9086i	−0.529251	−	0.848466i
$730$		0			0
$731$	8.07874	+	13.9928i	0.298803	+	0.517542i
$732$		0			0
$733$	−3.13184	−	1.80817i	−0.115677	−	0.0667863i	0.441045	−	0.897485i	$-0.354608\pi$
$733$	−3.13184	−	1.80817i	−0.115677	−	0.0667863i	−0.556722	+	0.830699i	$0.687941\pi$
$734$		0			0
$735$	−0.102925	−	1.75913i	−0.00379646	−	0.0648864i
$736$		0			0
$737$	11.0117	+	6.35763i	0.405623	+	0.234186i
$738$		0			0
$739$	19.3463	+	33.5087i	0.711665	+	1.23264i	0.964232	+	0.265060i	$0.0853917\pi$
$739$	19.3463	+	33.5087i	0.711665	+	1.23264i	−0.252567	+	0.967579i	$0.581275\pi$
$740$		0			0
$741$	−11.5745	−	9.60056i	−0.425201	−	0.352685i
$742$		0			0
$743$			45.1194i			1.65527i	0.561266	+	0.827635i	$0.310314\pi$
$743$			45.1194i			1.65527i	−0.561266	+	0.827635i	$0.689686\pi$
$744$		0			0
$745$	−1.12740	+	0.650904i	−0.0413047	+	0.0238473i
$746$		0			0
$747$	45.2375	+	15.8849i	1.65515	+	0.581197i
$748$		0			0
$749$	14.8286	−	10.9771i	0.541823	−	0.401094i
$750$		0			0
$751$	11.7841	−	20.4107i	0.430009	−	0.744797i	−0.566865	−	0.823811i	$-0.691844\pi$
$751$	11.7841	−	20.4107i	0.430009	−	0.744797i	0.996874	+	0.0790136i	$0.0251771\pi$
$752$		0			0
$753$	−1.01809	+	5.97226i	−0.0371013	+	0.217641i
$754$		0			0
$755$	−0.398610			−0.0145069
$756$		0			0
$757$	26.2967			0.955770			0.477885	−	0.878422i	$-0.341404\pi$
$757$	26.2967			0.955770			0.477885	+	0.878422i	$0.341404\pi$
$758$		0			0
$759$	6.19523	−	36.3421i	0.224872	−	1.31914i
$760$		0			0
$761$	12.9780	−	22.4785i	0.470452	−	0.814846i	−0.528977	−	0.848636i	$-0.677424\pi$
$761$	12.9780	−	22.4785i	0.470452	−	0.814846i	0.999429	+	0.0337898i	$0.0107577\pi$
$762$		0			0
$763$	−3.56218	+	0.406574i	−0.128960	+	0.0147190i
$764$		0			0
$765$	−0.722746	−	0.253787i	−0.0261309	−	0.00917570i
$766$		0			0
$767$	19.8114	−	11.4381i	0.715348	−	0.413006i
$768$		0			0
$769$		−	36.9215i		−	1.33142i	−0.746209	−	0.665712i	$-0.768128\pi$
$769$		−	36.9215i		−	1.33142i	0.746209	−	0.665712i	$-0.231872\pi$
$770$		0			0
$771$	−21.2444	−	17.6212i	−0.765097	−	0.634614i
$772$		0			0
$773$	5.79284	+	10.0335i	0.208354	+	0.360879i	0.951196	−	0.308587i	$-0.0998561\pi$
$773$	5.79284	+	10.0335i	0.208354	+	0.360879i	−0.742842	+	0.669466i	$0.766523\pi$
$774$		0			0
$775$	15.5247	+	8.96322i	0.557665	+	0.321968i
$776$		0			0
$777$	24.0019	−	12.1438i	0.861062	−	0.435655i
$778$		0			0
$779$	−19.6408	−	11.3396i	−0.703705	−	0.406284i
$780$		0			0
$781$	−9.62376	−	16.6688i	−0.344365	−	0.596458i
$782$		0			0
$783$	−32.2050	−	17.8681i	−1.15091	−	0.638555i
$784$		0			0
$785$		−	1.96861i		−	0.0702627i
$786$		0			0
$787$	25.9153	−	14.9622i	0.923779	−	0.533344i	0.0389406	−	0.999242i	$-0.487602\pi$
$787$	25.9153	−	14.9622i	0.923779	−	0.533344i	0.884839	+	0.465897i	$0.154268\pi$
$788$		0			0
$789$	8.63827	+	23.3200i	0.307531	+	0.830214i
$790$		0			0
$791$	−9.70609	−	4.21804i	−0.345109	−	0.149976i
$792$		0			0
$793$	−5.49653	+	9.52027i	−0.195188	+	0.338075i
$794$		0			0
$795$	1.28824	+	0.219605i	0.0456891	+	0.00778860i
$796$		0			0
$797$	20.2866			0.718587			0.359293	−	0.933225i	$-0.383018\pi$
$797$	20.2866			0.718587			0.359293	+	0.933225i	$0.383018\pi$
$798$		0			0
$799$	16.3453			0.578254
$800$		0			0
$801$	19.7676	−	16.9738i	0.698455	−	0.599740i
$802$		0			0
$803$	16.1148	−	27.9117i	0.568680	−	0.984982i
$804$		0			0
$805$	0.375799	+	3.29255i	0.0132452	+	0.116047i
$806$		0			0
$807$	11.9610	−	4.43062i	0.421046	−	0.155965i
$808$		0			0
$809$	−2.15641	+	1.24501i	−0.0758155	+	0.0437721i	−0.537429	−	0.843309i	$-0.680604\pi$
$809$	−2.15641	+	1.24501i	−0.0758155	+	0.0437721i	0.461613	+	0.887081i	$0.347271\pi$
$810$		0			0
$811$		−	15.9838i		−	0.561269i	−0.959815	−	0.280634i	$-0.909455\pi$
$811$		−	15.9838i		−	0.561269i	0.959815	−	0.280634i	$-0.0905448\pi$
$812$		0			0
$813$	13.8584	−	16.7078i	0.486036	−	0.585970i
$814$		0			0
$815$	0.294206	+	0.509581i	0.0103056	+	0.0178498i
$816$		0			0
$817$	33.8740	+	19.5572i	1.18510	+	0.684219i
$818$		0			0
$819$	−11.8818	−	11.0169i	−0.415183	−	0.384962i
$820$		0			0
$821$	2.38960	+	1.37963i	0.0833975	+	0.0481495i	0.541119	−	0.840946i	$-0.318001\pi$
$821$	2.38960	+	1.37963i	0.0833975	+	0.0481495i	−0.457721	+	0.889096i	$0.651334\pi$
$822$		0			0
$823$	14.2212	+	24.6318i	0.495720	+	0.858612i	0.999988	−	0.00493523i	$-0.00157094\pi$
$823$	14.2212	+	24.6318i	0.495720	+	0.858612i	−0.504268	+	0.863547i	$0.668238\pi$
$824$		0			0
$825$	13.5974	−	16.3932i	0.473401	−	0.570738i
$826$		0			0
$827$		−	30.6070i		−	1.06431i	−0.846647	−	0.532154i	$-0.821383\pi$
$827$		−	30.6070i		−	1.06431i	0.846647	−	0.532154i	$-0.178617\pi$
$828$		0			0
$829$	8.71397	−	5.03101i	0.302649	−	0.174734i	−0.340983	−	0.940069i	$-0.610760\pi$
$829$	8.71397	−	5.03101i	0.302649	−	0.174734i	0.643632	+	0.765335i	$0.277427\pi$
$830$		0			0
$831$	−52.7568	+	19.5424i	−1.83011	+	0.677917i
$832$		0			0
$833$	−3.59089	+	11.7619i	−0.124417	+	0.407527i
$834$		0			0
$835$	−0.269255	+	0.466363i	−0.00931794	+	0.0161391i
$836$		0			0
$837$	0.319139	+	18.7060i	0.0110310	+	0.646574i
$838$		0			0
$839$	13.3067			0.459400			0.229700	−	0.973262i	$-0.426226\pi$
$839$	13.3067			0.459400			0.229700	+	0.973262i	$0.426226\pi$
$840$		0			0
$841$	−21.2383			−0.732354
$842$		0			0
$843$	−17.3744	−	2.96180i	−0.598404	−	0.102010i
$844$		0			0
$845$	−0.641856	+	1.11173i	−0.0220805	+	0.0382446i
$846$		0			0
$847$	7.71380	+	10.4203i	0.265049	+	0.358045i
$848$		0			0
$849$	0.824393	+	2.22554i	0.0282931	+	0.0763805i
$850$		0			0
$851$	−43.8098	+	25.2936i	−1.50178	+	0.867053i
$852$		0			0
$853$		−	42.4736i		−	1.45427i	−0.686495	−	0.727134i	$-0.740852\pi$
$853$		−	42.4736i		−	1.45427i	0.686495	−	0.727134i	$-0.259148\pi$
$854$		0			0
$855$	−1.82242	+	0.342755i	−0.0623253	+	0.0117220i
$856$		0			0
$857$	4.77854	+	8.27667i	0.163232	+	0.282726i	0.936026	−	0.351931i	$-0.114475\pi$
$857$	4.77854	+	8.27667i	0.163232	+	0.282726i	−0.772794	+	0.634657i	$0.781142\pi$
$858$		0			0
$859$	−1.82940	−	1.05620i	−0.0624183	−	0.0360372i	0.468466	−	0.883481i	$-0.344807\pi$
$859$	−1.82940	−	1.05620i	−0.0624183	−	0.0360372i	−0.530884	+	0.847444i	$0.678140\pi$
$860$		0			0
$861$	−20.4565	−	13.3674i	−0.697156	−	0.455561i
$862$		0			0
$863$	−30.5684	−	17.6487i	−1.04056	−	0.600768i	−0.120569	−	0.992705i	$-0.538472\pi$
$863$	−30.5684	−	17.6487i	−1.04056	−	0.600768i	−0.919992	+	0.391936i	$0.871805\pi$
$864$		0			0
$865$	−1.63317	−	2.82873i	−0.0555294	−	0.0961797i
$866$		0			0
$867$	−18.5486	−	15.3853i	−0.629945	−	0.522511i
$868$		0			0
$869$		−	14.1308i		−	0.479356i
$870$		0			0
$871$	−9.10193	+	5.25500i	−0.308407	+	0.178059i
$872$		0			0
$873$	−6.61301	+	18.8328i	−0.223817	+	0.637394i
$874$		0			0
$875$	−1.52937	+	3.51922i	−0.0517022	+	0.118971i
$876$		0			0
$877$	8.36886	−	14.4953i	0.282596	−	0.489471i	−0.689427	−	0.724355i	$-0.742138\pi$
$877$	8.36886	−	14.4953i	0.282596	−	0.489471i	0.972023	+	0.234884i	$0.0754709\pi$
$878$		0			0
$879$	4.94694	−	29.0195i	0.166856	−	0.978803i
$880$		0			0
$881$	−42.6152			−1.43574			−0.717871	−	0.696176i	$-0.754883\pi$
$881$	−42.6152			−1.43574			−0.717871	+	0.696176i	$0.754883\pi$
$882$		0			0
$883$	−15.2392			−0.512839			−0.256419	−	0.966566i	$-0.582543\pi$
$883$	−15.2392			−0.512839			−0.256419	+	0.966566i	$0.582543\pi$
$884$		0			0
$885$	0.474043	−	2.78081i	0.0159348	−	0.0934758i
$886$		0			0
$887$	28.0633	−	48.6071i	0.942275	−	1.63207i	0.181157	−	0.983454i	$-0.442016\pi$
$887$	28.0633	−	48.6071i	0.942275	−	1.63207i	0.761118	−	0.648613i	$-0.224651\pi$
$888$		0			0
$889$	−7.73377	+	17.7961i	−0.259382	+	0.596862i
$890$		0			0
$891$	21.9724	+	3.36099i	0.736103	+	0.112597i
$892$		0			0
$893$	34.2677	−	19.7845i	1.14673	−	0.662062i
$894$		0			0
$895$			0.534639i			0.0178710i
$896$		0			0
$897$	23.4543	+	19.4543i	0.783116	+	0.649560i
$898$		0			0
$899$	12.7600	+	22.1009i	0.425569	+	0.737107i
$900$		0			0
$901$	−7.89836	−	4.56012i	−0.263132	−	0.151920i
$902$		0			0
$903$	35.2809	+	23.0545i	1.17407	+	0.767205i
$904$		0			0
$905$	−1.00827	−	0.582126i	−0.0335161	−	0.0193505i
$906$		0			0
$907$	−20.3625	−	35.2688i	−0.676124	−	1.17108i	−0.976139	−	0.217147i	$-0.930325\pi$
$907$	−20.3625	−	35.2688i	−0.676124	−	1.17108i	0.300015	−	0.953935i	$-0.403008\pi$
$908$		0			0
$909$	8.94266	+	47.5478i	0.296609	+	1.57706i
$910$		0			0
$911$		−	31.0308i		−	1.02810i	−0.857761	−	0.514049i	$-0.828145\pi$
$911$		−	31.0308i		−	1.02810i	0.857761	−	0.514049i	$-0.171855\pi$
$912$		0			0
$913$	−34.1833	+	19.7357i	−1.13130	+	0.653157i
$914$		0			0
$915$	0.470872	+	1.27117i	0.0155666	+	0.0420237i
$916$		0			0
$917$	−9.59719	−	12.9645i	−0.316927	−	0.428125i
$918$		0			0
$919$	25.6178	−	44.3713i	0.845053	−	1.46367i	−0.0405222	−	0.999179i	$-0.512902\pi$
$919$	25.6178	−	44.3713i	0.845053	−	1.46367i	0.885575	−	0.464496i	$-0.153765\pi$
$920$		0			0
$921$	−35.6890	−	6.08389i	−1.17599	−	0.200471i
$922$		0			0
$923$	15.9093			0.523662
$924$		0			0
$925$	−29.2253			−0.960922
$926$		0			0
$927$	0.332488	+	0.387214i	0.0109203	+	0.0127178i
$928$		0			0
$929$	−1.87116	+	3.24094i	−0.0613907	+	0.106332i	−0.895087	−	0.445891i	$-0.852887\pi$
$929$	−1.87116	+	3.24094i	−0.0613907	+	0.106332i	0.833697	+	0.552223i	$0.186220\pi$
$930$		0			0
$931$	6.70849	+	29.0052i	0.219862	+	0.950608i
$932$		0			0
$933$	−18.6471	+	6.90733i	−0.610480	+	0.226136i
$934$		0			0
$935$	0.546135	−	0.315311i	0.0178605	−	0.0103118i
$936$		0			0
$937$		−	3.23951i		−	0.105830i	−0.998599	−	0.0529150i	$-0.983149\pi$
$937$		−	3.23951i		−	0.105830i	0.998599	−	0.0529150i	$-0.0168512\pi$
$938$		0			0
$939$	10.9447	−	13.1951i	0.357168	−	0.430606i
$940$		0			0
$941$	−11.0342	−	19.1117i	−0.359703	−	0.623024i	0.628208	−	0.778046i	$-0.283789\pi$
$941$	−11.0342	−	19.1117i	−0.359703	−	0.623024i	−0.987911	+	0.155021i	$0.950455\pi$
$942$		0			0
$943$	39.7996	+	22.9783i	1.29605	+	0.748276i
$944$		0			0
$945$	−1.98103	+	0.260413i	−0.0644430	+	0.00847123i
$946$		0			0
$947$	31.4016	+	18.1297i	1.02042	+	0.589137i	0.914224	−	0.405208i	$-0.132801\pi$
$947$	31.4016	+	18.1297i	1.02042	+	0.589137i	0.106191	+	0.994346i	$0.466134\pi$
$948$		0			0
$949$	13.3200	+	23.0709i	0.432384	+	0.748912i
$950$		0			0
$951$	7.33606	−	8.84443i	0.237888	−	0.286800i
$952$		0			0
$953$			13.4656i			0.436192i	0.975927	+	0.218096i	$0.0699846\pi$
$953$			13.4656i			0.436192i	−0.975927	+	0.218096i	$0.930015\pi$
$954$		0			0
$955$	0.141171	−	0.0815052i	0.00456819	−	0.00263745i
$956$		0			0
$957$	28.4324	−	10.5320i	0.919090	−	0.340452i
$958$		0			0
$959$	6.02230	+	52.7640i	0.194470	+	1.70384i
$960$		0			0
$961$	−9.01821	+	15.6200i	−0.290910	+	0.503871i
$962$		0			0
$963$	−13.6283	−	15.8715i	−0.439166	−	0.511451i
$964$		0			0
$965$	2.66964			0.0859388
$966$		0			0
$967$	−9.25940			−0.297762			−0.148881	−	0.988855i	$-0.547567\pi$
$967$	−9.25940			−0.297762			−0.148881	+	0.988855i	$0.547567\pi$
$968$		0			0
$969$	12.7575	+	2.17477i	0.409830	+	0.0698636i
$970$		0			0
$971$	−19.9645	+	34.5795i	−0.640691	+	1.10971i	0.344587	+	0.938754i	$0.388019\pi$
$971$	−19.9645	+	34.5795i	−0.640691	+	1.10971i	−0.985279	+	0.170956i	$0.945314\pi$
$972$		0			0
$973$	0.285587	+	0.124109i	0.00915549	+	0.00397876i
$974$		0			0
$975$	6.11511	+	16.5084i	0.195840	+	0.528693i
$976$		0			0
$977$	−52.4299	+	30.2704i	−1.67738	+	0.968436i	−0.714060	+	0.700084i	$0.753146\pi$
$977$	−52.4299	+	30.2704i	−1.67738	+	0.968436i	−0.963321	+	0.268352i	$0.913521\pi$
$978$		0			0
$979$			21.4501i			0.685548i
$980$		0			0
$981$	0.751427	+	3.99531i	0.0239912	+	0.127560i
$982$		0			0
$983$	19.7027	+	34.1261i	0.628419	+	1.08845i	0.987869	+	0.155289i	$0.0496308\pi$
$983$	19.7027	+	34.1261i	0.628419	+	1.08845i	−0.359450	+	0.933164i	$0.617036\pi$
$984$		0			0
$985$	−0.0373445	−	0.0215609i	−0.00118990	−	0.000686987i
$986$		0			0
$987$	38.0433	−	19.2480i	1.21093	−	0.612671i
$988$		0			0
$989$	−68.6413	−	39.6301i	−2.18267	−	1.26016i
$990$		0			0
$991$	−15.0507	−	26.0686i	−0.478102	−	0.828098i	0.521583	−	0.853201i	$-0.325342\pi$
$991$	−15.0507	−	26.0686i	−0.478102	−	0.828098i	−0.999685	+	0.0251033i	$0.992009\pi$
$992$		0			0
$993$	19.6381	+	16.2889i	0.623196	+	0.516914i
$994$		0			0
$995$		−	3.97527i		−	0.126025i
$996$		0			0
$997$	−6.10467	+	3.52453i	−0.193337	+	0.111623i	−0.593544	−	0.804802i	$-0.702272\pi$
$997$	−6.10467	+	3.52453i	−0.193337	+	0.111623i	0.400207	+	0.916425i	$0.368938\pi$
$998$		0			0
$999$	−15.6987	−	26.1504i	−0.496685	−	0.827361i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.u.a.89.5	yes	16
3.2	odd	2	inner	168.2.u.a.89.7	yes	16
4.3	odd	2		336.2.bc.f.257.4		16
7.2	even	3		1176.2.k.a.881.14		16
7.3	odd	6	inner	168.2.u.a.17.7	yes	16
7.4	even	3		1176.2.u.b.521.2		16
7.5	odd	6		1176.2.k.a.881.3		16
7.6	odd	2		1176.2.u.b.1097.4		16
12.11	even	2		336.2.bc.f.257.2		16
21.2	odd	6		1176.2.k.a.881.4		16
21.5	even	6		1176.2.k.a.881.13		16
21.11	odd	6		1176.2.u.b.521.4		16
21.17	even	6	inner	168.2.u.a.17.5	✓	16
21.20	even	2		1176.2.u.b.1097.2		16
28.3	even	6		336.2.bc.f.17.2		16
28.19	even	6		2352.2.k.i.881.14		16
28.23	odd	6		2352.2.k.i.881.3		16
84.23	even	6		2352.2.k.i.881.13		16
84.47	odd	6		2352.2.k.i.881.4		16
84.59	odd	6		336.2.bc.f.17.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.u.a.17.5	✓	16	21.17	even	6	inner
168.2.u.a.17.7	yes	16	7.3	odd	6	inner
168.2.u.a.89.5	yes	16	1.1	even	1	trivial
168.2.u.a.89.7	yes	16	3.2	odd	2	inner
336.2.bc.f.17.2		16	28.3	even	6
336.2.bc.f.17.4		16	84.59	odd	6
336.2.bc.f.257.2		16	12.11	even	2
336.2.bc.f.257.4		16	4.3	odd	2
1176.2.k.a.881.3		16	7.5	odd	6
1176.2.k.a.881.4		16	21.2	odd	6
1176.2.k.a.881.13		16	21.5	even	6
1176.2.k.a.881.14		16	7.2	even	3
1176.2.u.b.521.2		16	7.4	even	3
1176.2.u.b.521.4		16	21.11	odd	6
1176.2.u.b.1097.2		16	21.20	even	2
1176.2.u.b.1097.4		16	7.6	odd	2
2352.2.k.i.881.3		16	28.23	odd	6
2352.2.k.i.881.4		16	84.47	odd	6
2352.2.k.i.881.13		16	84.23	even	6
2352.2.k.i.881.14		16	28.19	even	6

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.291063 - 1.70742i) q^{3} +(-0.0726693 + 0.125867i) q^{5} +(1.05451 - 2.42652i) q^{7} +(-2.83056 - 0.993934i) q^{9} +O(q^{10})\)	\(q+(0.291063 - 1.70742i) q^{3} +(-0.0726693 + 0.125867i) q^{5} +(1.05451 - 2.42652i) q^{7} +(-2.83056 - 0.993934i) q^{9} +(2.13889 - 1.23489i) q^{11} +2.04143i q^{13} +(0.193756 + 0.160712i) q^{15} +(-0.878419 - 1.52147i) q^{17} +(-3.68319 - 2.12649i) q^{19} +(-3.83616 - 2.50676i) q^{21} +(7.46351 + 4.30906i) q^{23} +(2.48944 + 4.31183i) q^{25} +(-2.52094 + 4.54366i) q^{27} +7.08790i q^{29} +(3.11812 - 1.80025i) q^{31} +(-1.48592 - 4.01141i) q^{33} +(0.228788 + 0.309061i) q^{35} +(-2.93493 + 5.08345i) q^{37} +(3.48558 + 0.594185i) q^{39} +5.33255 q^{41} -9.19692 q^{43} +(0.330798 - 0.284046i) q^{45} +(-4.65190 + 8.05733i) q^{47} +(-4.77602 - 5.11758i) q^{49} +(-2.85346 + 1.05699i) q^{51} +(4.49578 - 2.59564i) q^{53} +0.358953i q^{55} +(-4.70286 + 5.66982i) q^{57} +(-5.60299 - 9.70466i) q^{59} +(4.66353 + 2.69249i) q^{61} +(-5.39666 + 5.82031i) q^{63} +(-0.256949 - 0.148349i) q^{65} +(2.57417 + 4.45860i) q^{67} +(9.52973 - 11.4891i) q^{69} -7.79323i q^{71} +(11.3013 - 6.52482i) q^{73} +(8.08669 - 2.99550i) q^{75} +(-0.741003 - 6.49226i) q^{77} +(2.86075 - 4.95497i) q^{79} +(7.02419 + 5.62679i) q^{81} -15.9818 q^{83} +0.255336 q^{85} +(12.1020 + 2.06303i) q^{87} +(-4.34252 + 7.52147i) q^{89} +(4.95358 + 2.15271i) q^{91} +(-2.16621 - 5.84793i) q^{93} +(0.535310 - 0.309061i) q^{95} -6.65337i q^{97} +(-7.28165 + 1.36951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{7} + 2 q^{9}+O(q^{10}) \) 16 * q + 4 * q^7 + 2 * q^9	\( 16 q + 4 q^{7} + 2 q^{9} + 8 q^{15} - 6 q^{19} + 14 q^{21} - 18 q^{25} - 48 q^{31} - 12 q^{33} - 2 q^{37} - 22 q^{39} + 20 q^{43} - 42 q^{45} - 28 q^{49} + 6 q^{51} - 8 q^{57} + 36 q^{61} - 32 q^{63} + 14 q^{67} + 30 q^{73} + 54 q^{75} + 28 q^{79} + 30 q^{81} + 16 q^{85} + 78 q^{87} + 66 q^{91} + 16 q^{93} + 20 q^{99}+O(q^{100}) \) 16 * q + 4 * q^7 + 2 * q^9 + 8 * q^15 - 6 * q^19 + 14 * q^21 - 18 * q^25 - 48 * q^31 - 12 * q^33 - 2 * q^37 - 22 * q^39 + 20 * q^43 - 42 * q^45 - 28 * q^49 + 6 * q^51 - 8 * q^57 + 36 * q^61 - 32 * q^63 + 14 * q^67 + 30 * q^73 + 54 * q^75 + 28 * q^79 + 30 * q^81 + 16 * q^85 + 78 * q^87 + 66 * q^91 + 16 * q^93 + 20 * q^99

Introduction

L-functions

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Database

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