LMFDB - Embedded newform 168.2.u.a.17.7

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			17.7
Root			$-1.70742 + 0.291063i$ of defining polynomial
Character	$\chi$	$=$	168.17
Dual form			168.2.u.a.89.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.62420 - 0.601642i) q^{3} +(0.0726693 + 0.125867i) q^{5} +(1.05451 + 2.42652i) q^{7} +(2.27605 - 1.95437i) q^{9} +O(q^{10})$	\(q+(1.62420 - 0.601642i) q^{3} +(0.0726693 + 0.125867i) q^{5} +(1.05451 + 2.42652i) q^{7} +(2.27605 - 1.95437i) q^{9} +(-2.13889 - 1.23489i) q^{11} -2.04143i q^{13} +(0.193756 + 0.160712i) q^{15} +(0.878419 - 1.52147i) q^{17} +(-3.68319 + 2.12649i) q^{19} +(3.17263 + 3.30672i) q^{21} +(-7.46351 + 4.30906i) q^{23} +(2.48944 - 4.31183i) q^{25} +(2.52094 - 4.54366i) q^{27} +7.08790i q^{29} +(3.11812 + 1.80025i) q^{31} +(-4.21694 - 0.718860i) q^{33} +(-0.228788 + 0.309061i) q^{35} +(-2.93493 - 5.08345i) q^{37} +(-1.22821 - 3.31569i) q^{39} -5.33255 q^{41} -9.19692 q^{43} +(0.411390 + 0.144457i) q^{45} +(4.65190 + 8.05733i) q^{47} +(-4.77602 + 5.11758i) q^{49} +(0.511351 - 2.99966i) q^{51} +(-4.49578 - 2.59564i) q^{53} -0.358953i q^{55} +(-4.70286 + 5.66982i) q^{57} +(5.60299 - 9.70466i) q^{59} +(4.66353 - 2.69249i) q^{61} +(7.14245 + 3.46199i) q^{63} +(0.256949 - 0.148349i) q^{65} +(2.57417 - 4.45860i) q^{67} +(-9.52973 + 11.4891i) q^{69} -7.79323i q^{71} +(11.3013 + 6.52482i) q^{73} +(1.44917 - 8.50103i) q^{75} +(0.741003 - 6.49226i) q^{77} +(2.86075 + 4.95497i) q^{79} +(1.36085 - 8.89652i) q^{81} +15.9818 q^{83} +0.255336 q^{85} +(4.26437 + 11.5122i) q^{87} +(4.34252 + 7.52147i) q^{89} +(4.95358 - 2.15271i) q^{91} +(6.14756 + 1.04797i) q^{93} +(-0.535310 - 0.309061i) q^{95} +6.65337i q^{97} +(-7.28165 + 1.36951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

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

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
$3$	1.62420	−	0.601642i	0.937733	−	0.347358i
$3$	1.62420	−	0.601642i	0.937733	−	0.347358i
$4$		0			0
$5$	0.0726693	+	0.125867i	0.0324987	+	0.0562894i	0.881817	−	0.471591i	$-0.156320\pi$
$5$	0.0726693	+	0.125867i	0.0324987	+	0.0562894i	−0.849319	+	0.527881i	$0.822987\pi$
$6$		0			0
$7$	1.05451	+	2.42652i	0.398567	+	0.917139i
$7$	1.05451	+	2.42652i	0.398567	+	0.917139i
$8$		0			0
$9$	2.27605	−	1.95437i	0.758685	−	0.651458i
$10$		0			0
$11$	−2.13889	−	1.23489i	−0.644899	−	0.372332i	0.141600	−	0.989924i	$-0.454775\pi$
$11$	−2.13889	−	1.23489i	−0.644899	−	0.372332i	−0.786499	+	0.617592i	$0.788109\pi$
$12$		0			0
$13$		−	2.04143i		−	0.566191i	−0.959092	−	0.283096i	$-0.908639\pi$
$13$		−	2.04143i		−	0.566191i	0.959092	−	0.283096i	$-0.0913613\pi$
$14$		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	$-0.764994\pi$
$17$	0.878419	−	1.52147i	0.213048	−	0.369010i	0.952667	+	0.304016i	$0.0983276\pi$
$18$		0			0
$19$	−3.68319	+	2.12649i	−0.844983	+	0.487851i	−0.858955	−	0.512051i	$-0.828886\pi$
$19$	−3.68319	+	2.12649i	−0.844983	+	0.487851i	0.0139720	+	0.999902i	$0.495552\pi$
$20$		0			0
$21$	3.17263	+	3.30672i	0.692325	+	0.721586i
$22$		0			0
$23$	−7.46351	+	4.30906i	−1.55625	+	0.898501i	−0.558640	+	0.829410i	$0.688677\pi$
$23$	−7.46351	+	4.30906i	−1.55625	+	0.898501i	−0.997610	+	0.0690910i	$0.977990\pi$
$24$		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	0.753158	−	0.657840i	$-0.228530\pi$
$31$	3.11812	+	1.80025i	0.560031	+	0.323334i	−0.193127	+	0.981174i	$0.561863\pi$
$32$		0			0
$33$	−4.21694	−	0.718860i	−0.734075	−	0.125138i
$34$		0			0
$35$	−0.228788	+	0.309061i	−0.0386723	+	0.0522409i
$36$		0			0
$37$	−2.93493	−	5.08345i	−0.482499	−	0.835713i	0.517299	−	0.855805i	$-0.326938\pi$
$37$	−2.93493	−	5.08345i	−0.482499	−	0.835713i	−0.999798	+	0.0200916i	$0.993604\pi$
$38$		0			0
$39$	−1.22821	−	3.31569i	−0.196671	−	0.530936i
$40$		0			0
$41$	−5.33255			−0.832804			−0.416402	−	0.909181i	$-0.636709\pi$
$41$	−5.33255			−0.832804			−0.416402	+	0.909181i	$0.636709\pi$
$42$		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
$45$	0.411390	+	0.144457i	0.0613264	+	0.0215344i
$46$		0			0
$47$	4.65190	+	8.05733i	0.678549	+	1.17528i	0.975418	+	0.220364i	$0.0707244\pi$
$47$	4.65190	+	8.05733i	0.678549	+	1.17528i	−0.296868	+	0.954918i	$0.595942\pi$
$48$		0			0
$49$	−4.77602	+	5.11758i	−0.682288	+	0.731083i
$50$		0			0
$51$	0.511351	−	2.99966i	0.0716034	−	0.420036i
$52$		0			0
$53$	−4.49578	−	2.59564i	−0.617543	−	0.356539i	0.158369	−	0.987380i	$-0.449377\pi$
$53$	−4.49578	−	2.59564i	−0.617543	−	0.356539i	−0.775912	+	0.630841i	$0.782710\pi$
$54$		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	−0.227670	−	0.973738i	$-0.573111\pi$
$59$	5.60299	−	9.70466i	0.729447	−	1.26344i	0.957117	−	0.289701i	$-0.0935558\pi$
$60$		0			0
$61$	4.66353	−	2.69249i	0.597104	−	0.344738i	−0.170798	−	0.985306i	$-0.554634\pi$
$61$	4.66353	−	2.69249i	0.597104	−	0.344738i	0.767901	+	0.640568i	$0.221301\pi$
$62$		0			0
$63$	7.14245	+	3.46199i	0.899864	+	0.436170i
$64$		0			0
$65$	0.256949	−	0.148349i	0.0318705	−	0.0184005i
$66$		0			0
$67$	2.57417	−	4.45860i	0.314485	−	0.544705i	−0.664843	−	0.746984i	$-0.731501\pi$
$67$	2.57417	−	4.45860i	0.314485	−	0.544705i	0.979328	+	0.202279i	$0.0648347\pi$
$68$		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	0.984162	−	0.177273i	$-0.0567277\pi$
$73$	11.3013	+	6.52482i	1.32272	+	0.763672i	0.338558	+	0.940946i	$0.390061\pi$
$74$		0			0
$75$	1.44917	−	8.50103i	0.167335	−	0.981615i
$76$		0			0
$77$	0.741003	−	6.49226i	0.0844451	−	0.739861i
$78$		0			0
$79$	2.86075	+	4.95497i	0.321860	+	0.557478i	0.980872	−	0.194655i	$-0.0623586\pi$
$79$	2.86075	+	4.95497i	0.321860	+	0.557478i	−0.659012	+	0.752133i	$0.729025\pi$
$80$		0			0
$81$	1.36085	−	8.89652i	0.151205	−	0.988502i
$82$		0			0
$83$	15.9818			1.75423			0.877115	−	0.480280i	$-0.159465\pi$
$83$	15.9818			1.75423			0.877115	+	0.480280i	$0.159465\pi$
$84$		0			0
$85$	0.255336			0.0276951
$86$		0			0
$87$	4.26437	+	11.5122i	0.457189	+	1.23423i
$88$		0			0
$89$	4.34252	+	7.52147i	0.460306	+	0.797274i	0.998976	−	0.0452432i	$-0.0144063\pi$
$89$	4.34252	+	7.52147i	0.460306	+	0.797274i	−0.538670	+	0.842517i	$0.681073\pi$
$90$		0			0
$91$	4.95358	−	2.15271i	0.519276	−	0.225665i
$92$		0			0
$93$	6.14756	+	1.04797i	0.637472	+	0.108670i
$94$		0			0
$95$	−0.535310	−	0.309061i	−0.0549217	−	0.0317090i
$96$		0			0
$97$			6.65337i			0.675547i	0.941227	+	0.337774i	$0.109674\pi$
$97$			6.65337i			0.675547i	−0.941227	+	0.337774i	$0.890326\pi$
$98$		0			0
$99$	−7.28165	+	1.36951i	−0.731834	+	0.137641i
$100$		0			0
$101$	8.06357	−	13.9665i	0.802355	−	1.38972i	−0.115707	−	0.993283i	$-0.536913\pi$
$101$	8.06357	−	13.9665i	0.802355	−	1.38972i	0.918062	−	0.396437i	$-0.129753\pi$
$102$		0			0
$103$	−0.147333	+	0.0850626i	−0.0145171	+	0.00838147i	−0.507241	−	0.861804i	$-0.669335\pi$
$103$	−0.147333	+	0.0850626i	−0.0145171	+	0.00838147i	0.492724	+	0.870186i	$0.336001\pi$
$104$		0			0
$105$	−0.185654	+	0.639626i	−0.0181179	+	0.0624211i
$106$		0			0
$107$	−6.03900	+	3.48662i	−0.583813	+	0.337064i	−0.762647	−	0.646815i	$-0.776101\pi$
$107$	−6.03900	+	3.48662i	−0.583813	+	0.337064i	0.178835	+	0.983879i	$0.442767\pi$
$108$		0			0
$109$	−0.677559	+	1.17357i	−0.0648984	+	0.112407i	−0.896649	−	0.442742i	$-0.854006\pi$
$109$	−0.677559	+	1.17357i	−0.0648984	+	0.112407i	0.831751	+	0.555150i	$0.187339\pi$
$110$		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
$117$	−3.98972	−	4.64641i	−0.368850	−	0.429561i
$118$		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
$123$	−8.66113	+	3.20828i	−0.780948	+	0.289281i
$124$		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
$129$	−14.9376	+	5.53325i	−1.31519	+	0.487175i
$130$		0			0
$131$	−3.04832	−	5.27985i	−0.266333	−	0.461303i	0.701579	−	0.712592i	$-0.252479\pi$
$131$	−3.04832	−	5.27985i	−0.266333	−	0.461303i	−0.967912	+	0.251289i	$0.919146\pi$
$132$		0			0
$133$	−9.04395	−	6.69494i	−0.784210	−	0.580525i
$134$		0			0
$135$	0.755091	−	0.0128824i	0.0649879	−	0.00110874i
$136$		0			0
$137$	17.3832	+	10.0362i	1.48515	+	0.857451i	0.999857	−	0.0169018i	$-0.00538026\pi$
$137$	17.3832	+	10.0362i	1.48515	+	0.857451i	0.485291	+	0.874353i	$0.338714\pi$
$138$		0			0
$139$		−	0.117694i		−	0.00998266i	−0.999988	−	0.00499133i	$-0.998411\pi$
$139$		−	0.117694i		−	0.00998266i	0.999988	−	0.00499133i	$-0.00158880\pi$
$140$		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
$147$	−4.67826	+	11.1854i	−0.385856	+	0.922559i
$148$		0			0
$149$	−7.75705	+	4.47853i	−0.635482	+	0.366896i	−0.782872	−	0.622183i	$-0.786246\pi$
$149$	−7.75705	+	4.47853i	−0.635482	+	0.366896i	0.147390	+	0.989078i	$0.452913\pi$
$150$		0			0
$151$	1.37132	−	2.37519i	0.111596	−	0.193290i	−0.804818	−	0.593522i	$-0.797737\pi$
$151$	1.37132	−	2.37519i	0.111596	−	0.193290i	0.916414	+	0.400232i	$0.131070\pi$
$152$		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	−0.0474193	−	0.998875i	$-0.515100\pi$
$157$	−11.7303	−	6.77249i	−0.936180	−	0.540504i	−0.888761	+	0.458371i	$0.848433\pi$
$158$		0			0
$159$	−8.86370	−	1.51099i	−0.702937	−	0.119829i
$160$		0			0
$161$	−18.3264	−	13.5664i	−1.44432	−	1.06918i
$162$		0			0
$163$	2.02428	+	3.50616i	0.158554	+	0.274624i	0.934347	−	0.356363i	$-0.115983\pi$
$163$	2.02428	+	3.50616i	0.158554	+	0.274624i	−0.775793	+	0.630987i	$0.782650\pi$
$164$		0			0
$165$	−0.215961	−	0.583012i	−0.0168126	−	0.0453874i
$166$		0			0
$167$	−3.70521			−0.286717			−0.143359	−	0.989671i	$-0.545790\pi$
$167$	−3.70521			−0.286717			−0.143359	+	0.989671i	$0.545790\pi$
$168$		0			0
$169$	8.83256			0.679428
$170$		0			0
$171$	−4.22719	+	12.0384i	−0.323261	+	0.920596i
$172$		0			0
$173$	11.2370	+	19.4630i	0.854333	+	1.47975i	0.877263	+	0.480011i	$0.159367\pi$
$173$	11.2370	+	19.4630i	0.854333	+	1.47975i	−0.0229296	+	0.999737i	$0.507299\pi$
$174$		0			0
$175$	13.0879	+	1.49381i	0.989352	+	0.112921i
$176$		0			0
$177$	3.26165	−	19.1333i	0.245160	−	1.43815i
$178$		0			0
$179$	−3.18574	−	1.83929i	−0.238113	−	0.137475i	0.376196	−	0.926540i	$-0.377232\pi$
$179$	−3.18574	−	1.83929i	−0.238113	−	0.137475i	−0.614309	+	0.789065i	$0.710565\pi$
$180$		0			0
$181$		−	8.01062i		−	0.595425i	−0.954656	−	0.297712i	$-0.903776\pi$
$181$		−	8.01062i		−	0.595425i	0.954656	−	0.297712i	$-0.0962237\pi$
$182$		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
$189$	13.6837	+	1.32577i	0.995339	+	0.0964354i
$190$		0			0
$191$	0.971326	−	0.560795i	0.0702827	−	0.0405777i	−0.464447	−	0.885601i	$-0.653747\pi$
$191$	0.971326	−	0.560795i	0.0702827	−	0.0405777i	0.534730	+	0.845023i	$0.320413\pi$
$192$		0			0
$193$	−9.18421	+	15.9075i	−0.661094	+	1.14505i	0.319235	+	0.947676i	$0.396574\pi$
$193$	−9.18421	+	15.9075i	−0.661094	+	1.14505i	−0.980329	+	0.197373i	$0.936759\pi$
$194$		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	−0.962202	−	0.272336i	$-0.912204\pi$
$199$	−23.6874	−	13.6759i	−1.67915	−	0.969460i	−0.716951	−	0.697124i	$-0.754463\pi$
$200$		0			0
$201$	1.49850	−	8.79039i	0.105696	−	0.620027i
$202$		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
$207$	−8.56585	+	24.3942i	−0.595368	+	1.69551i
$208$		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
$213$	−4.68873	−	12.6578i	−0.321267	−	0.867296i
$214$		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
$219$	22.2812	+	3.79827i	1.50562	+	0.256663i
$220$		0			0
$221$	−3.10597	−	1.79323i	−0.208930	−	0.120626i
$222$		0			0
$223$		−	6.89447i		−	0.461688i	−0.972991	−	0.230844i	$-0.925851\pi$
$223$		−	6.89447i		−	0.461688i	0.972991	−	0.230844i	$-0.0741487\pi$
$224$		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	$-0.980194\pi$
$227$	−6.70734	+	11.6174i	−0.445182	+	0.771077i	0.552883	+	0.833259i	$0.313528\pi$
$228$		0			0
$229$	−5.51012	+	3.18127i	−0.364119	+	0.210224i	−0.670886	−	0.741560i	$-0.734086\pi$
$229$	−5.51012	+	3.18127i	−0.364119	+	0.210224i	0.306767	+	0.951785i	$0.400753\pi$
$230$		0			0
$231$	−2.70248	−	10.9905i	−0.177810	−	0.723125i
$232$		0			0
$233$	−4.29295	+	2.47853i	−0.281240	+	0.162374i	−0.633985	−	0.773346i	$-0.718582\pi$
$233$	−4.29295	+	2.47853i	−0.281240	+	0.162374i	0.352744	+	0.935720i	$0.385248\pi$
$234$		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	0.846688	−	0.532090i	$-0.178593\pi$
$241$	12.5626	+	7.25302i	0.809228	+	0.467208i	−0.0374597	+	0.999298i	$0.511927\pi$
$242$		0			0
$243$	−3.14223	−	15.2685i	−0.201574	−	0.979473i
$244$		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
$249$	25.9577	−	9.61532i	1.64500	−	0.609346i
$250$		0			0
$251$	3.49783			0.220781			0.110391	−	0.993888i	$-0.464790\pi$
$251$	3.49783			0.220781			0.110391	+	0.993888i	$0.464790\pi$
$252$		0			0
$253$	21.2848			1.33816
$254$		0			0
$255$	0.414717	−	0.153621i	0.0259706	−	0.00962012i
$256$		0			0
$257$	−7.96781	−	13.8006i	−0.497018	−	0.860861i	0.502976	−	0.864300i	$-0.332238\pi$
$257$	−7.96781	−	13.8006i	−0.497018	−	0.860861i	−0.999994	+	0.00343985i	$0.998905\pi$
$258$		0			0
$259$	9.24018	−	12.4822i	0.574157	−	0.775607i
$260$		0			0
$261$	13.8524	+	16.1324i	0.857442	+	0.998573i
$262$		0			0
$263$	12.4343	+	7.17892i	0.766729	+	0.442671i	0.831706	−	0.555216i	$-0.187364\pi$
$263$	12.4343	+	7.17892i	0.766729	+	0.442671i	−0.0649777	+	0.997887i	$0.520698\pi$
$264$		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	$-0.905409\pi$
$269$	−3.68211	+	6.37760i	−0.224502	+	0.388849i	0.731668	+	0.681661i	$0.238742\pi$
$270$		0			0
$271$	10.8537	−	6.26636i	0.659313	−	0.380654i	−0.132702	−	0.991156i	$-0.542365\pi$
$271$	10.8537	−	6.26636i	0.659313	−	0.380654i	0.792015	+	0.610501i	$0.209032\pi$
$272$		0			0
$273$	6.75044	−	6.47671i	0.408555	−	0.391988i
$274$		0			0
$275$	−10.6493	+	6.14835i	−0.642174	+	0.370759i
$276$		0			0
$277$	−16.2409	+	28.1300i	−0.975819	+	1.69017i	−0.298614	+	0.954374i	$0.596524\pi$
$277$	−16.2409	+	28.1300i	−0.975819	+	1.69017i	−0.677205	+	0.735794i	$0.736809\pi$
$278$		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	0.464315	−	0.885670i	$-0.346300\pi$
$283$	−1.18666	−	0.685120i	−0.0705397	−	0.0407261i	−0.534855	+	0.844944i	$0.679634\pi$
$284$		0			0
$285$	−1.05540	−	0.179913i	−0.0625162	−	0.0106571i
$286$		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
$291$	4.00295	+	10.8064i	0.234657	+	0.633483i
$292$		0			0
$293$	−16.9961			−0.992923			−0.496461	−	0.868059i	$-0.665368\pi$
$293$	−16.9961			−0.992923			−0.496461	+	0.868059i	$0.665368\pi$
$294$		0			0
$295$	1.62866			0.0948243
$296$		0			0
$297$	−11.0029	+	6.60531i	−0.638453	+	0.383279i
$298$		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
$303$	4.69402	−	27.5358i	0.269664	−	1.58189i
$304$		0			0
$305$	0.677791	+	0.391323i	0.0388102	+	0.0224071i
$306$		0			0
$307$			20.9023i			1.19296i	0.802629	+	0.596479i	$0.203434\pi$
$307$			20.9023i			1.19296i	−0.802629	+	0.596479i	$0.796566\pi$
$308$		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	$-0.727798\pi$
$311$	5.74040	−	9.94267i	0.325508	−	0.563797i	0.981615	+	0.190871i	$0.0611312\pi$
$312$		0			0
$313$	8.57172	−	4.94889i	0.484502	−	0.279728i	−0.237788	−	0.971317i	$-0.576423\pi$
$313$	8.57172	−	4.94889i	0.484502	−	0.279728i	0.722291	+	0.691589i	$0.243089\pi$
$314$		0			0
$315$	0.0832870	+	1.15058i	0.00469269	+	0.0648278i
$316$		0			0
$317$	−5.74547	+	3.31715i	−0.322698	+	0.186310i	−0.652594	−	0.757707i	$-0.726319\pi$
$317$	−5.74547	+	3.31715i	−0.322698	+	0.186310i	0.329897	+	0.944017i	$0.392986\pi$
$318$		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
$327$	−0.394425	+	2.31376i	−0.0218118	+	0.127951i
$328$		0			0
$329$	−14.6458	+	19.7845i	−0.807449	+	1.09075i
$330$		0			0
$331$	−7.36537	−	12.7572i	−0.404837	−	0.701199i	0.589465	−	0.807794i	$-0.299339\pi$
$331$	−7.36537	−	12.7572i	−0.404837	−	0.701199i	−0.994303	+	0.106595i	$0.966005\pi$
$332$		0			0
$333$	−16.6150	−	5.83425i	−0.910497	−	0.319715i
$334$		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
$339$	−2.40657	−	6.49680i	−0.130707	−	0.352858i
$340$		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
$345$	−2.13862	−	0.364570i	−0.115139	−	0.0196278i
$346$		0			0
$347$	14.5124	+	8.37875i	0.779068	+	0.449795i	0.836100	−	0.548577i	$-0.184830\pi$
$347$	14.5124	+	8.37875i	0.779068	+	0.449795i	−0.0570320	+	0.998372i	$0.518164\pi$
$348$		0			0
$349$			3.12385i			0.167216i	0.996499	+	0.0836080i	$0.0266443\pi$
$349$			3.12385i			0.167216i	−0.996499	+	0.0836080i	$0.973356\pi$
$350$		0			0
$351$	−9.27558	−	5.14632i	−0.495094	−	0.274690i
$352$		0			0
$353$	−17.7450	+	30.7353i	−0.944473	+	1.63587i	−0.187669	+	0.982232i	$0.560093\pi$
$353$	−17.7450	+	30.7353i	−0.944473	+	1.63587i	−0.756804	+	0.653642i	$0.773240\pi$
$354$		0			0
$355$	0.980910	−	0.566328i	0.0520613	−	0.0300576i
$356$		0			0
$357$	7.81796	−	1.92237i	0.413770	−	0.101742i
$358$		0			0
$359$	5.42817	−	3.13395i	0.286488	−	0.165404i	−0.349869	−	0.936799i	$-0.613774\pi$
$359$	5.42817	−	3.13395i	0.286488	−	0.165404i	0.636357	+	0.771395i	$0.280441\pi$
$360$		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	0.0685342	−	0.997649i	$-0.478168\pi$
$367$	−14.5823	−	8.41907i	−0.761188	−	0.439472i	−0.829722	+	0.558177i	$0.811501\pi$
$368$		0			0
$369$	−12.1372	+	10.4218i	−0.631836	+	0.542537i
$370$		0			0
$371$	1.55753	−	13.6462i	0.0808631	−	0.708478i
$372$		0			0
$373$	0.617106	+	1.06886i	0.0319526	+	0.0553435i	0.881559	−	0.472073i	$-0.156494\pi$
$373$	0.617106	+	1.06886i	0.0319526	+	0.0553435i	−0.849607	+	0.527416i	$0.823161\pi$
$374$		0			0
$375$	2.35560	−	0.872570i	0.121643	−	0.0450593i
$376$		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
$381$	−11.9119	+	4.41244i	−0.610264	+	0.226056i
$382$		0			0
$383$	4.95842	+	8.58824i	0.253364	+	0.438839i	0.964450	−	0.264266i	$-0.0851298\pi$
$383$	4.95842	+	8.58824i	0.253364	+	0.438839i	−0.711086	+	0.703105i	$0.751796\pi$
$384$		0			0
$385$	0.871008	−	0.378520i	0.0443907	−	0.0192912i
$386$		0			0
$387$	−20.9327	+	17.9742i	−1.06407	+	0.913680i
$388$		0			0
$389$	−11.5061	−	6.64306i	−0.583383	−	0.336816i	0.179094	−	0.983832i	$-0.442683\pi$
$389$	−11.5061	−	6.64306i	−0.583383	−	0.336816i	−0.762477	+	0.647016i	$0.776017\pi$
$390$		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	0.131691	−	0.991291i	$-0.457959\pi$
$397$	21.0410	−	12.1480i	1.05602	−	0.609693i	0.924328	+	0.381598i	$0.124626\pi$
$398$		0			0
$399$	−18.7171	−	5.43271i	−0.937029	−	0.271976i
$400$		0			0
$401$	12.4125	−	7.16635i	0.619850	−	0.357870i	−0.156961	−	0.987605i	$-0.550170\pi$
$401$	12.4125	−	7.16635i	0.619850	−	0.357870i	0.776810	+	0.629735i	$0.216836\pi$
$402$		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	0.862904	−	0.505368i	$-0.168643\pi$
$409$	17.3256	+	10.0029i	0.856695	+	0.494613i	−0.00620937	+	0.999981i	$0.501977\pi$
$410$		0			0
$411$	34.2720	+	5.84234i	1.69051	+	0.288181i
$412$		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
$417$	−0.0708095	−	0.191158i	−0.00346756	−	0.00936107i
$418$		0			0
$419$	−27.7445			−1.35541			−0.677704	−	0.735335i	$-0.737025\pi$
$419$	−27.7445			−1.35541			−0.677704	+	0.735335i	$0.737025\pi$
$420$		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
$423$	26.3350	+	9.24737i	1.28045	+	0.449622i
$424$		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
$429$	−1.46750	+	8.60859i	−0.0708517	+	0.415627i
$430$		0			0
$431$	−14.8277	−	8.56080i	−0.714227	−	0.412359i	0.0983974	−	0.995147i	$-0.468628\pi$
$431$	−14.8277	−	8.56080i	−0.714227	−	0.412359i	−0.812624	+	0.582788i	$0.801962\pi$
$432$		0			0
$433$		−	27.5219i		−	1.32262i	−0.750113	−	0.661310i	$-0.770001\pi$
$433$		−	27.5219i		−	1.32262i	0.750113	−	0.661310i	$-0.229999\pi$
$434$		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	−0.879286	−	0.476294i	$-0.841980\pi$
$439$	−18.9922	+	10.9651i	−0.906446	+	0.523337i	−0.0271602	+	0.999631i	$0.508646\pi$
$440$		0			0
$441$	−0.868806	+	20.9820i	−0.0413717	+	0.999144i
$442$		0			0
$443$	17.7589	−	10.2531i	0.843750	−	0.487139i	−0.0147873	−	0.999891i	$-0.504707\pi$
$443$	17.7589	−	10.2531i	0.843750	−	0.487139i	0.858537	+	0.512752i	$0.171374\pi$
$444$		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
$453$	0.798279	−	4.68282i	0.0375064	−	0.220018i
$454$		0			0
$455$	0.630928	+	0.467055i	0.0295783	+	0.0218959i
$456$		0			0
$457$	−3.79670	−	6.57607i	−0.177602	−	0.307616i	0.763457	−	0.645859i	$-0.223501\pi$
$457$	−3.79670	−	6.57607i	−0.177602	−	0.307616i	−0.941059	+	0.338243i	$0.890167\pi$
$458$		0			0
$459$	−4.69859	−	7.82676i	−0.219312	−	0.365322i
$460$		0			0
$461$	29.2727			1.36337			0.681683	−	0.731648i	$-0.261248\pi$
$461$	29.2727			1.36337			0.681683	+	0.731648i	$0.261248\pi$
$462$		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
$465$	0.314834	+	0.849930i	0.0146001	+	0.0394146i
$466$		0			0
$467$	−2.58282	−	4.47358i	−0.119519	−	0.207013i	0.800058	−	0.599922i	$-0.204802\pi$
$467$	−2.58282	−	4.47358i	−0.119519	−	0.207013i	−0.919577	+	0.392910i	$0.871469\pi$
$468$		0			0
$469$	13.5334	+	1.54465i	0.624914	+	0.0713254i
$470$		0			0
$471$	−23.1270	−	3.94245i	−1.06563	−	0.181658i
$472$		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	$-0.684656\pi$
$479$	9.85496	−	17.0693i	0.450284	−	0.779915i	0.998403	+	0.0564848i	$0.0179893\pi$
$480$		0			0
$481$	−10.3775	+	5.99145i	−0.473173	+	0.273187i
$482$		0			0
$483$	−37.9278	−	11.0087i	−1.72578	−	0.500913i
$484$		0			0
$485$	−0.837439	+	0.483496i	−0.0380261	+	0.0219544i
$486$		0			0
$487$	2.50360	−	4.33637i	0.113449	−	0.196500i	−0.803710	−	0.595022i	$-0.797143\pi$
$487$	2.50360	−	4.33637i	0.113449	−	0.196500i	0.917159	+	0.398522i	$0.130477\pi$
$488$		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
$495$	−0.701529	−	0.816997i	−0.0315314	−	0.0367213i
$496$		0			0
$497$	18.9104	−	8.21804i	0.848249	−	0.368629i
$498$		0			0
$499$	0.404702	+	0.700965i	0.0181170	+	0.0313795i	0.874942	−	0.484228i	$-0.160900\pi$
$499$	0.404702	+	0.700965i	0.0181170	+	0.0313795i	−0.856825	+	0.515608i	$0.827566\pi$
$500$		0			0
$501$	−6.01800	+	2.22921i	−0.268864	+	0.0995936i
$502$		0			0
$503$	9.47070			0.422278			0.211139	−	0.977456i	$-0.432283\pi$
$503$	9.47070			0.422278			0.211139	+	0.977456i	$0.432283\pi$
$504$		0			0
$505$	2.34390			0.104302
$506$		0			0
$507$	14.3458	−	5.31404i	0.637122	−	0.236005i
$508$		0			0
$509$	−5.24404	−	9.08294i	−0.232438	−	0.402594i	0.726087	−	0.687603i	$-0.241337\pi$
$509$	−5.24404	−	9.08294i	−0.232438	−	0.402594i	−0.958525	+	0.285009i	$0.908004\pi$
$510$		0			0
$511$	−3.91526	+	34.3034i	−0.173201	+	1.51749i
$512$		0			0
$513$	0.376973	+	22.0960i	0.0166438	+	0.975560i
$514$		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	$-0.900469\pi$
$521$	−4.77854	+	8.27667i	−0.209351	+	0.362607i	0.742159	+	0.670224i	$0.233802\pi$
$522$		0			0
$523$	−24.0305	+	13.8740i	−1.05078	+	0.606668i	−0.922868	−	0.385117i	$-0.874161\pi$
$523$	−24.0305	+	13.8740i	−1.05078	+	0.606668i	−0.127912	+	0.991785i	$0.540828\pi$
$524$		0			0
$525$	22.1561	−	5.44799i	0.966972	−	0.237770i
$526$		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
$537$	−6.28087	−	1.07070i	−0.271040	−	0.0462040i
$538$		0			0
$539$	16.5350	−	5.04809i	0.712213	−	0.217437i
$540$		0			0
$541$	0.577777	+	1.00074i	0.0248406	+	0.0430251i	0.878178	−	0.478333i	$-0.158759\pi$
$541$	0.577777	+	1.00074i	0.0248406	+	0.0430251i	−0.853338	+	0.521358i	$0.825426\pi$
$542$		0			0
$543$	−4.81953	−	13.0109i	−0.206826	−	0.558349i
$544$		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
$549$	5.35232	−	15.2425i	0.228431	−	0.650536i
$550$		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
$555$	0.248311	−	1.45663i	0.0105402	−	0.0618304i
$556$		0			0
$557$	−32.1074	−	18.5372i	−1.36043	−	0.785447i	−0.370753	−	0.928732i	$-0.620900\pi$
$557$	−32.1074	−	18.5372i	−1.36043	−	0.785447i	−0.989682	+	0.143284i	$0.954234\pi$
$558$		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	$-0.726772\pi$
$563$	7.79584	−	13.5028i	0.328556	−	0.569075i	0.982225	+	0.187705i	$0.0601049\pi$
$564$		0			0
$565$	0.503468	−	0.290677i	0.0211810	−	0.0122289i
$566$		0			0
$567$	23.0226	−	6.07934i	0.966860	−	0.255308i
$568$		0			0
$569$	13.0276	−	7.52147i	0.546144	−	0.315316i	−0.201421	−	0.979505i	$-0.564556\pi$
$569$	13.0276	−	7.52147i	0.546144	−	0.315316i	0.747565	+	0.664188i	$0.231223\pi$
$570$		0			0
$571$	−2.81334	+	4.87284i	−0.117735	+	0.203922i	−0.918870	−	0.394561i	$-0.870897\pi$
$571$	−2.81334	+	4.87284i	−0.117735	+	0.203922i	0.801135	+	0.598484i	$0.204230\pi$
$572$		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	0.843634	−	0.536919i	$-0.180412\pi$
$577$	19.2278	+	11.1012i	0.800465	+	0.462149i	−0.0431688	+	0.999068i	$0.513745\pi$
$578$		0			0
$579$	−5.34637	+	31.3626i	−0.222188	+	1.30339i
$580$		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
$585$	0.294899	−	0.839825i	0.0121926	−	0.0347225i
$586$		0			0
$587$	−20.9245			−0.863648			−0.431824	−	0.901958i	$-0.642130\pi$
$587$	−20.9245			−0.863648			−0.431824	+	0.901958i	$0.642130\pi$
$588$		0			0
$589$	−15.3129			−0.630956
$590$		0			0
$591$	0.178506	+	0.481898i	0.00734277	+	0.0198226i
$592$		0			0
$593$	10.5845	+	18.3329i	0.434654	+	0.752842i	0.997267	−	0.0738778i	$-0.0235375\pi$
$593$	10.5845	+	18.3329i	0.434654	+	0.752842i	−0.562614	+	0.826720i	$0.690204\pi$
$594$		0			0
$595$	0.269255	+	0.619579i	0.0110384	+	0.0254003i
$596$		0			0
$597$	−46.7010	−	7.96111i	−1.91135	−	0.325826i
$598$		0			0
$599$	4.58648	+	2.64801i	0.187399	+	0.108195i	0.590764	−	0.806844i	$-0.298826\pi$
$599$	4.58648	+	2.64801i	0.187399	+	0.108195i	−0.403366	+	0.915039i	$0.632160\pi$
$600$		0			0
$601$		−	37.5346i		−	1.53107i	−0.643396	−	0.765533i	$-0.722475\pi$
$601$		−	37.5346i		−	1.53107i	0.643396	−	0.765533i	$-0.277525\pi$
$602$		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	0.395474	−	0.918477i	$-0.370580\pi$
$607$	34.2123	−	19.7525i	1.38864	−	0.801729i	0.993162	+	0.116748i	$0.0372469\pi$
$608$		0			0
$609$	−23.4377	+	22.4873i	−0.949743	+	0.911231i
$610$		0			0
$611$	16.4485	−	9.49653i	0.665434	−	0.384189i
$612$		0			0
$613$	−7.19736	+	12.4662i	−0.290699	+	0.503505i	−0.973975	−	0.226655i	$-0.927221\pi$
$613$	−7.19736	+	12.4662i	−0.290699	+	0.503505i	0.683277	+	0.730160i	$0.260554\pi$
$614$		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	0.120983	−	0.992655i	$-0.461395\pi$
$619$	−16.8732	−	9.74173i	−0.678190	−	0.391553i	−0.799173	+	0.601101i	$0.794729\pi$
$620$		0			0
$621$	0.763888	+	44.7746i	0.0306538	+	1.79674i
$622$		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
$627$	17.0605	−	6.31959i	0.681329	−	0.252380i
$628$		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
$633$	34.1561	−	12.6522i	1.35758	−	0.502880i
$634$		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
$639$	−15.2309	−	17.7378i	−0.602525	−	0.701697i
$640$		0			0
$641$	−36.0118	−	20.7914i	−1.42238	−	0.821211i	−0.425878	−	0.904781i	$-0.640035\pi$
$641$	−36.0118	−	20.7914i	−1.42238	−	0.821211i	−0.996502	+	0.0835697i	$0.973368\pi$
$642$		0			0
$643$		−	13.5290i		−	0.533531i	−0.963761	−	0.266766i	$-0.914045\pi$
$643$		−	13.5290i		−	0.533531i	0.963761	−	0.266766i	$-0.0859549\pi$
$644$		0			0
$645$	−1.78196	−	1.47806i	−0.0701646	−	0.0581984i
$646$		0			0
$647$	−15.0442	+	26.0573i	−0.591449	+	1.02442i	0.402589	+	0.915381i	$0.368110\pi$
$647$	−15.0442	+	26.0573i	−0.591449	+	1.02442i	−0.994038	+	0.109038i	$0.965223\pi$
$648$		0			0
$649$	−23.9683	+	13.8381i	−0.940839	+	0.543193i
$650$		0			0
$651$	3.93974	+	16.0223i	0.154410	+	0.627963i
$652$		0			0
$653$	−18.3717	+	10.6069i	−0.718941	+	0.415081i	−0.814363	−	0.580356i	$-0.802913\pi$
$653$	−18.3717	+	10.6069i	−0.718941	+	0.415081i	0.0954221	+	0.995437i	$0.469580\pi$
$654$		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	0.590397	−	0.807113i	$-0.298971\pi$
$661$	4.79785	+	2.77004i	0.186615	+	0.107742i	−0.403782	+	0.914855i	$0.632305\pi$
$662$		0			0
$663$	−6.12360	−	1.04389i	−0.237821	−	0.0405412i
$664$		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
$669$	−4.14800	−	11.1980i	−0.160371	−	0.432940i
$670$		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
$675$	−13.3158	−	22.1810i	−0.512526	−	0.853748i
$676$		0			0
$677$	−7.23319	−	12.5283i	−0.277994	−	0.481500i	0.692892	−	0.721041i	$-0.256336\pi$
$677$	−7.23319	−	12.5283i	−0.277994	−	0.481500i	−0.970886	+	0.239541i	$0.923003\pi$
$678$		0			0
$679$	−16.1446	+	7.01605i	−0.619571	+	0.269251i
$680$		0			0
$681$	−3.90452	+	22.9045i	−0.149621	+	0.877702i
$682$		0			0
$683$	−28.1356	−	16.2441i	−1.07658	−	0.621564i	−0.146609	−	0.989195i	$-0.546836\pi$
$683$	−28.1356	−	16.2441i	−1.07658	−	0.621564i	−0.929972	+	0.367630i	$0.880169\pi$
$684$		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	−0.927861	−	0.372927i	$-0.878354\pi$
$691$	−28.0961	+	16.2213i	−1.06883	+	0.617087i	−0.140966	+	0.990014i	$0.545021\pi$
$692$		0			0
$693$	−11.0017	−	16.2249i	−0.417921	−	0.616334i
$694$		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
$705$	−0.393576	+	2.30877i	−0.0148229	+	0.0869535i
$706$		0			0
$707$	42.3932	+	4.83860i	1.59436	+	0.181974i
$708$		0			0
$709$	16.2569	+	28.1578i	0.610542	+	1.05749i	0.991149	+	0.132753i	$0.0423816\pi$
$709$	16.2569	+	28.1578i	0.610542	+	1.05749i	−0.380607	+	0.924737i	$0.624285\pi$
$710$		0			0
$711$	16.1951	+	5.68680i	0.607364	+	0.213272i
$712$		0			0
$713$	−31.0295			−1.16207
$714$		0			0
$715$	−0.732778			−0.0274044
$716$		0			0
$717$	−10.4539	−	28.2215i	−0.390408	−	1.05395i
$718$		0			0
$719$	5.29867	+	9.17757i	0.197607	+	0.342266i	0.947752	−	0.319008i	$-0.103350\pi$
$719$	5.29867	+	9.17757i	0.197607	+	0.342266i	−0.750145	+	0.661273i	$0.770016\pi$
$720$		0			0
$721$	−0.361770	−	0.267807i	−0.0134730	−	0.00997365i
$722$		0			0
$723$	24.7679	+	4.22217i	0.921128	+	0.157024i
$724$		0			0
$725$	30.5618	+	17.6449i	1.13504	+	0.655314i
$726$		0			0
$727$		−	31.3600i		−	1.16308i	−0.813518	−	0.581540i	$-0.802451\pi$
$727$		−	31.3600i		−	1.16308i	0.813518	−	0.581540i	$-0.197549\pi$
$728$		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	−0.556722	−	0.830699i	$-0.687941\pi$
$733$	−3.13184	+	1.80817i	−0.115677	+	0.0667863i	0.441045	+	0.897485i	$0.354608\pi$
$734$		0			0
$735$	−1.74784	+	0.224000i	−0.0644701	+	0.00826235i
$736$		0			0
$737$	−11.0117	+	6.35763i	−0.405623	+	0.234186i
$738$		0			0
$739$	19.3463	−	33.5087i	0.711665	−	1.23264i	−0.252567	−	0.967579i	$-0.581275\pi$
$739$	19.3463	−	33.5087i	0.711665	−	1.23264i	0.964232	−	0.265060i	$-0.0853917\pi$
$740$		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
$747$	36.3755	−	31.2344i	1.33091	−	1.14281i
$748$		0			0
$749$	−14.8286	−	10.9771i	−0.541823	−	0.401094i
$750$		0			0
$751$	11.7841	+	20.4107i	0.430009	+	0.744797i	0.996874	−	0.0790136i	$-0.0251771\pi$
$751$	11.7841	+	20.4107i	0.430009	+	0.744797i	−0.566865	+	0.823811i	$0.691844\pi$
$752$		0			0
$753$	5.68118	−	2.10444i	0.207034	−	0.0766901i
$754$		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
$759$	34.5708	−	12.8058i	1.25484	−	0.464822i
$760$		0			0
$761$	−12.9780	−	22.4785i	−0.470452	−	0.814846i	0.528977	−	0.848636i	$-0.322576\pi$
$761$	−12.9780	−	22.4785i	−0.470452	−	0.814846i	−0.999429	+	0.0337898i	$0.989242\pi$
$762$		0			0
$763$	−3.56218	−	0.406574i	−0.128960	−	0.0147190i
$764$		0			0
$765$	0.581159	−	0.499022i	0.0210119	−	0.0180422i
$766$		0			0
$767$	−19.8114	−	11.4381i	−0.715348	−	0.413006i
$768$		0			0
$769$			36.9215i			1.33142i	0.746209	+	0.665712i	$0.231872\pi$
$769$			36.9215i			1.33142i	−0.746209	+	0.665712i	$0.768128\pi$
$770$		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	$-0.900144\pi$
$773$	−5.79284	+	10.0335i	−0.208354	+	0.360879i	0.742842	+	0.669466i	$0.233477\pi$
$774$		0			0
$775$	15.5247	−	8.96322i	0.557665	−	0.321968i
$776$		0			0
$777$	7.49808	−	25.8329i	0.268992	−	0.926750i
$778$		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	0.884839	−	0.465897i	$-0.154268\pi$
$787$	25.9153	+	14.9622i	0.923779	+	0.533344i	0.0389406	+	0.999242i	$0.487602\pi$
$788$		0			0
$789$	24.5149	+	4.17904i	0.872752	+	0.148778i
$790$		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
$795$	−0.453935	−	1.22545i	−0.0160994	−	0.0434622i
$796$		0			0
$797$	−20.2866			−0.718587			−0.359293	−	0.933225i	$-0.616982\pi$
$797$	−20.2866			−0.718587			−0.359293	+	0.933225i	$0.616982\pi$
$798$		0			0
$799$	16.3453			0.578254
$800$		0			0
$801$	24.5836	+	8.63236i	0.868618	+	0.305009i
$802$		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
$807$	−2.14345	+	12.5738i	−0.0754531	+	0.442619i
$808$		0			0
$809$	2.15641	+	1.24501i	0.0758155	+	0.0437721i	0.537429	−	0.843309i	$-0.319396\pi$
$809$	2.15641	+	1.24501i	0.0758155	+	0.0437721i	−0.461613	+	0.887081i	$0.652729\pi$
$810$		0			0
$811$			15.9838i			0.561269i	0.959815	+	0.280634i	$0.0905448\pi$
$811$			15.9838i			0.561269i	−0.959815	+	0.280634i	$0.909455\pi$
$812$		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
$819$	7.06741	−	14.5808i	0.246955	−	0.509495i
$820$		0			0
$821$	−2.38960	+	1.37963i	−0.0833975	+	0.0481495i	−0.541119	−	0.840946i	$-0.681999\pi$
$821$	−2.38960	+	1.37963i	−0.0833975	+	0.0481495i	0.457721	+	0.889096i	$0.348666\pi$
$822$		0			0
$823$	14.2212	−	24.6318i	0.495720	−	0.858612i	−0.504268	−	0.863547i	$-0.668238\pi$
$823$	14.2212	−	24.6318i	0.495720	−	0.858612i	0.999988	+	0.00493523i	$0.00157094\pi$
$824$		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	0.643632	−	0.765335i	$-0.277427\pi$
$829$	8.71397	+	5.03101i	0.302649	+	0.174734i	−0.340983	+	0.940069i	$0.610760\pi$
$830$		0			0
$831$	−9.45424	+	55.4599i	−0.327964	+	1.92388i
$832$		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
$837$	16.0403	−	9.62939i	0.554434	−	0.332840i
$838$		0			0
$839$	−13.3067			−0.459400			−0.229700	−	0.973262i	$-0.573774\pi$
$839$	−13.3067			−0.459400			−0.229700	+	0.973262i	$0.573774\pi$
$840$		0			0
$841$	−21.2383			−0.732354
$842$		0			0
$843$	−6.12218	−	16.5275i	−0.210859	−	0.569238i
$844$		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
$849$	−2.33957	−	0.398826i	−0.0802940	−	0.0136877i
$850$		0			0
$851$	43.8098	+	25.2936i	1.50178	+	0.867053i
$852$		0			0
$853$			42.4736i			1.45427i	0.686495	+	0.727134i	$0.259148\pi$
$853$			42.4736i			1.45427i	−0.686495	+	0.727134i	$0.740852\pi$
$854$		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	$-0.885525\pi$
$857$	−4.77854	+	8.27667i	−0.163232	+	0.282726i	0.772794	+	0.634657i	$0.218858\pi$
$858$		0			0
$859$	−1.82940	+	1.05620i	−0.0624183	+	0.0360372i	−0.530884	−	0.847444i	$-0.678140\pi$
$859$	−1.82940	+	1.05620i	−0.0624183	+	0.0360372i	0.468466	+	0.883481i	$0.344807\pi$
$860$		0			0
$861$	−16.9182	−	17.6333i	−0.576571	−	0.600940i
$862$		0			0
$863$	30.5684	−	17.6487i	1.04056	−	0.600768i	0.120569	−	0.992705i	$-0.461528\pi$
$863$	30.5684	−	17.6487i	1.04056	−	0.600768i	0.919992	+	0.391936i	$0.128195\pi$
$864$		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
$873$	13.0032	+	15.1434i	0.440091	+	0.512528i
$874$		0			0
$875$	1.52937	+	3.51922i	0.0517022	+	0.118971i
$876$		0			0
$877$	8.36886	+	14.4953i	0.282596	+	0.489471i	0.972023	−	0.234884i	$-0.0754709\pi$
$877$	8.36886	+	14.4953i	0.282596	+	0.489471i	−0.689427	+	0.724355i	$0.742138\pi$
$878$		0			0
$879$	−27.6051	+	10.2256i	−0.931096	+	0.344900i
$880$		0			0
$881$	42.6152			1.43574			0.717871	−	0.696176i	$-0.245117\pi$
$881$	42.6152			1.43574			0.717871	+	0.696176i	$0.245117\pi$
$882$		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
$885$	2.64527	−	0.979870i	0.0889198	−	0.0329380i
$886$		0			0
$887$	−28.0633	−	48.6071i	−0.942275	−	1.63207i	−0.761118	−	0.648613i	$-0.775349\pi$
$887$	−28.0633	−	48.6071i	−0.942275	−	1.63207i	−0.181157	−	0.983454i	$-0.557984\pi$
$888$		0			0
$889$	−7.73377	−	17.7961i	−0.259382	−	0.596862i
$890$		0			0
$891$	−13.8969	+	17.3482i	−0.465564	+	0.581185i
$892$		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
$903$	−29.1784	−	30.4116i	−0.970998	−	1.01204i
$904$		0			0
$905$	1.00827	−	0.582126i	0.0335161	−	0.0193505i
$906$		0			0
$907$	−20.3625	+	35.2688i	−0.676124	+	1.17108i	0.300015	+	0.953935i	$0.403008\pi$
$907$	−20.3625	+	35.2688i	−0.676124	+	1.17108i	−0.976139	+	0.217147i	$0.930325\pi$
$908$		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
$915$	1.33630	+	0.227799i	0.0441769	+	0.00753081i
$916$		0			0
$917$	9.59719	−	12.9645i	0.316927	−	0.428125i
$918$		0			0
$919$	25.6178	+	44.3713i	0.845053	+	1.46367i	0.885575	+	0.464496i	$0.153765\pi$
$919$	25.6178	+	44.3713i	0.845053	+	1.46367i	−0.0405222	+	0.999179i	$0.512902\pi$
$920$		0			0
$921$	12.5757	+	33.9495i	0.414383	+	1.11868i
$922$		0			0
$923$	−15.9093			−0.523662
$924$		0			0
$925$	−29.2253			−0.960922
$926$		0			0
$927$	−0.169093	+	0.481550i	−0.00555375	+	0.0158162i
$928$		0			0
$929$	1.87116	+	3.24094i	0.0613907	+	0.106332i	0.895087	−	0.445891i	$-0.147113\pi$
$929$	1.87116	+	3.24094i	0.0613907	+	0.106332i	−0.833697	+	0.552223i	$0.813780\pi$
$930$		0			0
$931$	6.70849	−	29.0052i	0.219862	−	0.950608i
$932$		0			0
$933$	3.34164	−	19.6026i	0.109400	−	0.641759i
$934$		0			0
$935$	−0.546135	−	0.315311i	−0.0178605	−	0.0103118i
$936$		0			0
$937$			3.23951i			0.105830i	0.998599	+	0.0529150i	$0.0168512\pi$
$937$			3.23951i			0.105830i	−0.998599	+	0.0529150i	$0.983149\pi$
$938$		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	$-0.716211\pi$
$941$	11.0342	−	19.1117i	0.359703	−	0.623024i	0.987911	+	0.155021i	$0.0495446\pi$
$942$		0			0
$943$	39.7996	−	22.9783i	1.29605	−	0.748276i
$944$		0			0
$945$	0.827511	+	1.81866i	0.0269189	+	0.0591611i
$946$		0			0
$947$	−31.4016	+	18.1297i	−1.02042	+	0.589137i	−0.914224	−	0.405208i	$-0.867199\pi$
$947$	−31.4016	+	18.1297i	−1.02042	+	0.589137i	−0.106191	+	0.994346i	$0.533866\pi$
$948$		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
$957$	5.09521	−	29.8892i	0.164705	−	0.966182i
$958$		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
$963$	−6.93094	+	19.7382i	−0.223347	+	0.636055i
$964$		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
$969$	4.49535	+	12.1357i	0.144411	+	0.389855i
$970$		0			0
$971$	19.9645	+	34.5795i	0.640691	+	1.10971i	0.985279	+	0.170956i	$0.0546856\pi$
$971$	19.9645	+	34.5795i	0.640691	+	1.10971i	−0.344587	+	0.938754i	$0.611981\pi$
$972$		0			0
$973$	0.285587	−	0.124109i	0.00915549	−	0.00397876i
$974$		0			0
$975$	−17.3543	−	2.95838i	−0.555781	−	0.0947439i
$976$		0			0
$977$	52.4299	+	30.2704i	1.67738	+	0.968436i	0.963321	+	0.268352i	$0.0864791\pi$
$977$	52.4299	+	30.2704i	1.67738	+	0.968436i	0.714060	+	0.700084i	$0.246854\pi$
$978$		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	0.359450	+	0.933164i	$0.382964\pi$
$983$	−19.7027	+	34.1261i	−0.628419	+	1.08845i	−0.987869	+	0.155289i	$0.950369\pi$
$984$		0			0
$985$	−0.0373445	+	0.0215609i	−0.00118990	+	0.000686987i
$986$		0			0
$987$	−11.8846	+	40.9455i	−0.378290	+	1.30331i
$988$		0			0
$989$	68.6413	−	39.6301i	2.18267	−	1.26016i
$990$		0			0
$991$	−15.0507	+	26.0686i	−0.478102	+	0.828098i	−0.999685	−	0.0251033i	$-0.992009\pi$
$991$	−15.0507	+	26.0686i	−0.478102	+	0.828098i	0.521583	+	0.853201i	$0.325342\pi$
$992$		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	0.400207	−	0.916425i	$-0.368938\pi$
$997$	−6.10467	−	3.52453i	−0.193337	−	0.111623i	−0.593544	+	0.804802i	$0.702272\pi$
$998$		0			0
$999$	−30.4962	+	0.520289i	−0.964858	+	0.0164612i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.u.a.17.5	✓	16	3.2	odd	2	inner
168.2.u.a.17.7	yes	16	1.1	even	1	trivial
168.2.u.a.89.5	yes	16	7.5	odd	6	inner
168.2.u.a.89.7	yes	16	21.5	even	6	inner
336.2.bc.f.17.2		16	4.3	odd	2
336.2.bc.f.17.4		16	12.11	even	2
336.2.bc.f.257.2		16	84.47	odd	6
336.2.bc.f.257.4		16	28.19	even	6
1176.2.k.a.881.3		16	7.4	even	3
1176.2.k.a.881.4		16	21.17	even	6
1176.2.k.a.881.13		16	21.11	odd	6
1176.2.k.a.881.14		16	7.3	odd	6
1176.2.u.b.521.2		16	7.6	odd	2
1176.2.u.b.521.4		16	21.20	even	2
1176.2.u.b.1097.2		16	21.2	odd	6
1176.2.u.b.1097.4		16	7.2	even	3
2352.2.k.i.881.3		16	28.3	even	6
2352.2.k.i.881.4		16	84.11	even	6
2352.2.k.i.881.13		16	84.59	odd	6
2352.2.k.i.881.14		16	28.11	odd	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)

\(f(q)\)	\(=\)	\(q+(1.62420 - 0.601642i) q^{3} +(0.0726693 + 0.125867i) q^{5} +(1.05451 + 2.42652i) q^{7} +(2.27605 - 1.95437i) q^{9} +O(q^{10})\)	\(q+(1.62420 - 0.601642i) q^{3} +(0.0726693 + 0.125867i) q^{5} +(1.05451 + 2.42652i) q^{7} +(2.27605 - 1.95437i) q^{9} +(-2.13889 - 1.23489i) q^{11} -2.04143i q^{13} +(0.193756 + 0.160712i) q^{15} +(0.878419 - 1.52147i) q^{17} +(-3.68319 + 2.12649i) q^{19} +(3.17263 + 3.30672i) q^{21} +(-7.46351 + 4.30906i) q^{23} +(2.48944 - 4.31183i) q^{25} +(2.52094 - 4.54366i) q^{27} +7.08790i q^{29} +(3.11812 + 1.80025i) q^{31} +(-4.21694 - 0.718860i) q^{33} +(-0.228788 + 0.309061i) q^{35} +(-2.93493 - 5.08345i) q^{37} +(-1.22821 - 3.31569i) q^{39} -5.33255 q^{41} -9.19692 q^{43} +(0.411390 + 0.144457i) q^{45} +(4.65190 + 8.05733i) q^{47} +(-4.77602 + 5.11758i) q^{49} +(0.511351 - 2.99966i) q^{51} +(-4.49578 - 2.59564i) q^{53} -0.358953i q^{55} +(-4.70286 + 5.66982i) q^{57} +(5.60299 - 9.70466i) q^{59} +(4.66353 - 2.69249i) q^{61} +(7.14245 + 3.46199i) q^{63} +(0.256949 - 0.148349i) q^{65} +(2.57417 - 4.45860i) q^{67} +(-9.52973 + 11.4891i) q^{69} -7.79323i q^{71} +(11.3013 + 6.52482i) q^{73} +(1.44917 - 8.50103i) q^{75} +(0.741003 - 6.49226i) q^{77} +(2.86075 + 4.95497i) q^{79} +(1.36085 - 8.89652i) q^{81} +15.9818 q^{83} +0.255336 q^{85} +(4.26437 + 11.5122i) q^{87} +(4.34252 + 7.52147i) q^{89} +(4.95358 - 2.15271i) q^{91} +(6.14756 + 1.04797i) q^{93} +(-0.535310 - 0.309061i) q^{95} +6.65337i q^{97} +(-7.28165 + 1.36951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{7} + 2 q^{9}+O(q^{10}) \) 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

Modular forms

Varieties

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Database

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