LMFDB - Embedded newform 336.2.bc.f.257.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(17,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, 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("336.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bc (of order $6$, degree $2$, not 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:	$2.68297350792$
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:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.2
Root			$-0.601642 + 1.62420i$ of defining polynomial
Character	$\chi$	$=$	336.257
Dual form			336.2.bc.f.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.62420 - 0.601642i) q^{3} +(0.0726693 - 0.125867i) q^{5} +(-1.05451 + 2.42652i) q^{7} +(2.27605 + 1.95437i) q^{9} +O(q^{10})$	\(q+(-1.62420 - 0.601642i) q^{3} +(0.0726693 - 0.125867i) q^{5} +(-1.05451 + 2.42652i) q^{7} +(2.27605 + 1.95437i) q^{9} +(2.13889 - 1.23489i) q^{11} +2.04143i q^{13} +(-0.193756 + 0.160712i) q^{15} +(0.878419 + 1.52147i) q^{17} +(3.68319 + 2.12649i) q^{19} +(3.17263 - 3.30672i) q^{21} +(7.46351 + 4.30906i) q^{23} +(2.48944 + 4.31183i) q^{25} +(-2.52094 - 4.54366i) q^{27} -7.08790i q^{29} +(-3.11812 + 1.80025i) q^{31} +(-4.21694 + 0.718860i) q^{33} +(0.228788 + 0.309061i) q^{35} +(-2.93493 + 5.08345i) q^{37} +(1.22821 - 3.31569i) q^{39} -5.33255 q^{41} +9.19692 q^{43} +(0.411390 - 0.144457i) q^{45} +(-4.65190 + 8.05733i) q^{47} +(-4.77602 - 5.11758i) q^{49} +(-0.511351 - 2.99966i) q^{51} +(-4.49578 + 2.59564i) q^{53} -0.358953i q^{55} +(-4.70286 - 5.66982i) q^{57} +(-5.60299 - 9.70466i) q^{59} +(4.66353 + 2.69249i) q^{61} +(-7.14245 + 3.46199i) q^{63} +(0.256949 + 0.148349i) q^{65} +(-2.57417 - 4.45860i) q^{67} +(-9.52973 - 11.4891i) q^{69} -7.79323i q^{71} +(11.3013 - 6.52482i) q^{73} +(-1.44917 - 8.50103i) q^{75} +(0.741003 + 6.49226i) q^{77} +(-2.86075 + 4.95497i) q^{79} +(1.36085 + 8.89652i) q^{81} -15.9818 q^{83} +0.255336 q^{85} +(-4.26437 + 11.5122i) q^{87} +(4.34252 - 7.52147i) q^{89} +(-4.95358 - 2.15271i) q^{91} +(6.14756 - 1.04797i) q^{93} +(0.535310 - 0.309061i) q^{95} -6.65337i q^{97} +(7.28165 + 1.36951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−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	−0.849319	−	0.527881i	$-0.822987\pi$
$5$	0.0726693	−	0.125867i	0.0324987	−	0.0562894i	0.881817	+	0.471591i	$0.156320\pi$
$6$		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	$-0.545225\pi$
$11$	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	0.952667	−	0.304016i	$-0.0983276\pi$
$17$	0.878419	+	1.52147i	0.213048	+	0.369010i	−0.739619	+	0.673026i	$0.764994\pi$
$18$		0			0
$19$	3.68319	+	2.12649i	0.844983	+	0.487851i	0.858955	−	0.512051i	$-0.171114\pi$
$19$	3.68319	+	2.12649i	0.844983	+	0.487851i	−0.0139720	+	0.999902i	$0.504448\pi$
$20$		0			0
$21$	3.17263	−	3.30672i	0.692325	−	0.721586i
$22$		0			0
$23$	7.46351	+	4.30906i	1.55625	+	0.898501i	0.997610	+	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	$-0.771363\pi$
$29$		−	7.08790i		−	1.31619i	0.752935	−	0.658095i	$-0.228637\pi$
$30$		0			0
$31$	−3.11812	+	1.80025i	−0.560031	+	0.323334i	−0.753158	−	0.657840i	$-0.771470\pi$
$31$	−3.11812	+	1.80025i	−0.560031	+	0.323334i	0.193127	+	0.981174i	$0.438137\pi$
$32$		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	−0.999798	−	0.0200916i	$-0.993604\pi$
$37$	−2.93493	+	5.08345i	−0.482499	+	0.835713i	0.517299	+	0.855805i	$0.326938\pi$
$38$		0			0
$39$	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	$-0.252622\pi$
$43$	9.19692			1.40252			0.701258	+	0.712907i	$0.252622\pi$
$44$		0			0
$45$	0.411390	−	0.144457i	0.0613264	−	0.0215344i
$46$		0			0
$47$	−4.65190	+	8.05733i	−0.678549	+	1.17528i	0.296868	+	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
$51$	−0.511351	−	2.99966i	−0.0716034	−	0.420036i
$52$		0			0
$53$	−4.49578	+	2.59564i	−0.617543	+	0.356539i	−0.775912	−	0.630841i	$-0.782710\pi$
$53$	−4.49578	+	2.59564i	−0.617543	+	0.356539i	0.158369	+	0.987380i	$0.449377\pi$
$54$		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
$63$	−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	$-0.268499\pi$
$67$	−2.57417	−	4.45860i	−0.314485	−	0.544705i	−0.979328	+	0.202279i	$0.935165\pi$
$68$		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
$75$	−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	$-0.937641\pi$
$79$	−2.86075	+	4.95497i	−0.321860	+	0.557478i	0.659012	+	0.752133i	$0.270975\pi$
$80$		0			0
$81$	1.36085	+	8.89652i	0.151205	+	0.988502i
$82$		0			0
$83$	−15.9818			−1.75423			−0.877115	−	0.480280i	$-0.840535\pi$
$83$	−15.9818			−1.75423			−0.877115	+	0.480280i	$0.840535\pi$
$84$		0			0
$85$	0.255336			0.0276951
$86$		0			0
$87$	−4.26437	+	11.5122i	−0.457189	+	1.23423i
$88$		0			0
$89$	4.34252	−	7.52147i	0.460306	−	0.797274i	−0.538670	−	0.842517i	$-0.681073\pi$
$89$	4.34252	−	7.52147i	0.460306	−	0.797274i	0.998976	+	0.0452432i	$0.0144063\pi$
$90$		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	$-0.890326\pi$
$97$		−	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	$0.129753\pi$
$101$	8.06357	+	13.9665i	0.802355	+	1.38972i	−0.115707	+	0.993283i	$0.536913\pi$
$102$		0			0
$103$	0.147333	+	0.0850626i	0.0145171	+	0.00838147i	0.507241	−	0.861804i	$-0.330665\pi$
$103$	0.147333	+	0.0850626i	0.0145171	+	0.00838147i	−0.492724	+	0.870186i	$0.663999\pi$
$104$		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	$-0.223899\pi$
$107$	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	$0.0602472\pi$
$113$			4.00000i			0.376288i	−0.982141	+	0.188144i	$0.939753\pi$
$114$		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	$-0.394503\pi$
$127$	7.33399			0.650787			0.325393	+	0.945579i	$0.394503\pi$
$128$		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	$-0.747521\pi$
$131$	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
$135$	−0.755091	−	0.0128824i	−0.0649879	−	0.00110874i
$136$		0			0
$137$	17.3832	−	10.0362i	1.48515	−	0.857451i	0.485291	−	0.874353i	$-0.338714\pi$
$137$	17.3832	−	10.0362i	1.48515	−	0.857451i	0.999857	+	0.0169018i	$0.00538026\pi$
$138$		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	0.147390	−	0.989078i	$-0.452913\pi$
$149$	−7.75705	−	4.47853i	−0.635482	−	0.366896i	−0.782872	+	0.622183i	$0.786246\pi$
$150$		0			0
$151$	−1.37132	−	2.37519i	−0.111596	−	0.193290i	0.804818	−	0.593522i	$-0.202263\pi$
$151$	−1.37132	−	2.37519i	−0.111596	−	0.193290i	−0.916414	+	0.400232i	$0.868930\pi$
$152$		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
$159$	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	$-0.884017\pi$
$163$	−2.02428	+	3.50616i	−0.158554	+	0.274624i	0.775793	+	0.630987i	$0.217350\pi$
$164$		0			0
$165$	−0.215961	+	0.583012i	−0.0168126	+	0.0453874i
$166$		0			0
$167$	3.70521			0.286717			0.143359	−	0.989671i	$-0.454210\pi$
$167$	3.70521			0.286717			0.143359	+	0.989671i	$0.454210\pi$
$168$		0			0
$169$	8.83256			0.679428
$170$		0			0
$171$	4.22719	+	12.0384i	0.323261	+	0.920596i
$172$		0			0
$173$	11.2370	−	19.4630i	0.854333	−	1.47975i	−0.0229296	−	0.999737i	$-0.507299\pi$
$173$	11.2370	−	19.4630i	0.854333	−	1.47975i	0.877263	−	0.480011i	$-0.159367\pi$
$174$		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	$-0.622768\pi$
$179$	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
$189$	13.6837	−	1.32577i	0.995339	−	0.0964354i
$190$		0			0
$191$	−0.971326	−	0.560795i	−0.0702827	−	0.0405777i	0.464447	−	0.885601i	$-0.346253\pi$
$191$	−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	$-0.996636\pi$
$197$		−	0.296699i		−	0.0211389i	0.999944	−	0.0105695i	$-0.00336442\pi$
$198$		0			0
$199$	23.6874	−	13.6759i	1.67915	−	0.969460i	0.716951	−	0.697124i	$-0.245537\pi$
$199$	23.6874	−	13.6759i	1.67915	−	0.969460i	0.962202	−	0.272336i	$-0.0877962\pi$
$200$		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	$-0.757636\pi$
$211$	−21.0295			−1.44773			−0.723864	+	0.689942i	$0.757636\pi$
$212$		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	$-0.0198058\pi$
$227$	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
$231$	2.70248	−	10.9905i	0.177810	−	0.723125i
$232$		0			0
$233$	−4.29295	−	2.47853i	−0.281240	−	0.162374i	0.352744	−	0.935720i	$-0.385248\pi$
$233$	−4.29295	−	2.47853i	−0.281240	−	0.162374i	−0.633985	+	0.773346i	$0.718582\pi$
$234$		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
$243$	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	$-0.535210\pi$
$251$	−3.49783			−0.220781			−0.110391	+	0.993888i	$0.535210\pi$
$252$		0			0
$253$	21.2848			1.33816
$254$		0			0
$255$	−0.414717	−	0.153621i	−0.0259706	−	0.00962012i
$256$		0			0
$257$	−7.96781	+	13.8006i	−0.497018	+	0.860861i	−0.999994	−	0.00343985i	$-0.998905\pi$
$257$	−7.96781	+	13.8006i	−0.497018	+	0.860861i	0.502976	+	0.864300i	$0.332238\pi$
$258$		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	$-0.812636\pi$
$263$	−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	0.731668	−	0.681661i	$-0.238742\pi$
$269$	−3.68211	−	6.37760i	−0.224502	−	0.388849i	−0.956170	+	0.292812i	$0.905409\pi$
$270$		0			0
$271$	−10.8537	−	6.26636i	−0.659313	−	0.380654i	0.132702	−	0.991156i	$-0.457635\pi$
$271$	−10.8537	−	6.26636i	−0.659313	−	0.380654i	−0.792015	+	0.610501i	$0.790968\pi$
$272$		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	−0.677205	−	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	$0.0981614\pi$
$281$			10.1758i			0.607037i	−0.952826	+	0.303518i	$0.901839\pi$
$282$		0			0
$283$	1.18666	−	0.685120i	0.0705397	−	0.0407261i	−0.464315	−	0.885670i	$-0.653700\pi$
$283$	1.18666	−	0.685120i	0.0705397	−	0.0407261i	0.534855	+	0.844944i	$0.320366\pi$
$284$		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	$-0.272202\pi$
$311$	−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
$315$	−0.0832870	+	1.15058i	−0.00469269	+	0.0648278i
$316$		0			0
$317$	−5.74547	−	3.31715i	−0.322698	−	0.186310i	0.329897	−	0.944017i	$-0.392986\pi$
$317$	−5.74547	−	3.31715i	−0.322698	−	0.186310i	−0.652594	+	0.757707i	$0.726319\pi$
$318$		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	$-0.700661\pi$
$331$	7.36537	−	12.7572i	0.404837	−	0.701199i	0.994303	+	0.106595i	$0.0339948\pi$
$332$		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	$-0.815170\pi$
$347$	−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	$-0.773240\pi$
$353$	−17.7450	−	30.7353i	−0.944473	−	1.63587i	−0.187669	−	0.982232i	$-0.560093\pi$
$354$		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	$-0.386226\pi$
$359$	−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	−0.0685342	−	0.997649i	$-0.521832\pi$
$367$	14.5823	−	8.41907i	0.761188	−	0.439472i	0.829722	+	0.558177i	$0.188499\pi$
$368$		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	−0.849607	−	0.527416i	$-0.823161\pi$
$373$	0.617106	−	1.06886i	0.0319526	−	0.0553435i	0.881559	+	0.472073i	$0.156494\pi$
$374$		0			0
$375$	−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	$-0.379505\pi$
$379$	14.3895			0.739141			0.369571	+	0.929203i	$0.379505\pi$
$380$		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	$-0.914870\pi$
$383$	−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
$387$	20.9327	+	17.9742i	1.06407	+	0.913680i
$388$		0			0
$389$	−11.5061	+	6.64306i	−0.583383	+	0.336816i	−0.762477	−	0.647016i	$-0.776017\pi$
$389$	−11.5061	+	6.64306i	−0.583383	+	0.336816i	0.179094	+	0.983832i	$0.442683\pi$
$390$		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
$399$	18.7171	−	5.43271i	0.937029	−	0.271976i
$400$		0			0
$401$	12.4125	+	7.16635i	0.619850	+	0.357870i	0.776810	−	0.629735i	$-0.216836\pi$
$401$	12.4125	+	7.16635i	0.619850	+	0.357870i	−0.156961	+	0.987605i	$0.550170\pi$
$402$		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
$411$	−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	$-0.262975\pi$
$419$	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
$423$	−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	$-0.531372\pi$
$431$	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	0.879286	−	0.476294i	$-0.158020\pi$
$439$	18.9922	+	10.9651i	0.906446	+	0.523337i	0.0271602	+	0.999631i	$0.491354\pi$
$440$		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	$-0.495293\pi$
$443$	−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	$0.146046\pi$
$449$			18.7692i			0.885773i	−0.896578	+	0.442886i	$0.853954\pi$
$450$		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	−0.941059	−	0.338243i	$-0.890167\pi$
$457$	−3.79670	+	6.57607i	−0.177602	+	0.307616i	0.763457	+	0.645859i	$0.223501\pi$
$458$		0			0
$459$	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	$-0.588662\pi$
$463$	−11.8326			−0.549906			−0.274953	+	0.961458i	$0.588662\pi$
$464$		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	$-0.795198\pi$
$467$	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
$471$	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	$-0.315344\pi$
$479$	−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
$483$	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	$-0.202857\pi$
$487$	−2.50360	−	4.33637i	−0.113449	−	0.196500i	−0.917159	+	0.398522i	$0.869523\pi$
$488$		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	$-0.839100\pi$
$499$	−0.404702	+	0.700965i	−0.0181170	+	0.0313795i	0.856825	+	0.515608i	$0.172434\pi$
$500$		0			0
$501$	−6.01800	−	2.22921i	−0.268864	−	0.0995936i
$502$		0			0
$503$	−9.47070			−0.422278			−0.211139	−	0.977456i	$-0.567717\pi$
$503$	−9.47070			−0.422278			−0.211139	+	0.977456i	$0.567717\pi$
$504$		0			0
$505$	2.34390			0.104302
$506$		0			0
$507$	−14.3458	−	5.31404i	−0.637122	−	0.236005i
$508$		0			0
$509$	−5.24404	+	9.08294i	−0.232438	+	0.402594i	−0.958525	−	0.285009i	$-0.908004\pi$
$509$	−5.24404	+	9.08294i	−0.232438	+	0.402594i	0.726087	+	0.687603i	$0.241337\pi$
$510$		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	0.742159	−	0.670224i	$-0.233802\pi$
$521$	−4.77854	−	8.27667i	−0.209351	−	0.362607i	−0.951510	+	0.307617i	$0.900469\pi$
$522$		0			0
$523$	24.0305	+	13.8740i	1.05078	+	0.606668i	0.922868	−	0.385117i	$-0.125839\pi$
$523$	24.0305	+	13.8740i	1.05078	+	0.606668i	0.127912	+	0.991785i	$0.459172\pi$
$524$		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	−0.853338	−	0.521358i	$-0.825426\pi$
$541$	0.577777	−	1.00074i	0.0248406	−	0.0430251i	0.878178	+	0.478333i	$0.158759\pi$
$542$		0			0
$543$	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	$-0.612133\pi$
$547$	−16.1394			−0.690070			−0.345035	+	0.938590i	$0.612133\pi$
$548$		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	−0.989682	−	0.143284i	$-0.954234\pi$
$557$	−32.1074	+	18.5372i	−1.36043	+	0.785447i	−0.370753	+	0.928732i	$0.620900\pi$
$558$		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
$567$	−23.0226	−	6.07934i	−0.966860	−	0.255308i
$568$		0			0
$569$	13.0276	+	7.52147i	0.546144	+	0.315316i	0.747565	−	0.664188i	$-0.231223\pi$
$569$	13.0276	+	7.52147i	0.546144	+	0.315316i	−0.201421	+	0.979505i	$0.564556\pi$
$570$		0			0
$571$	2.81334	+	4.87284i	0.117735	+	0.203922i	0.918870	−	0.394561i	$-0.129103\pi$
$571$	2.81334	+	4.87284i	0.117735	+	0.203922i	−0.801135	+	0.598484i	$0.795770\pi$
$572$		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
$579$	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	$-0.357870\pi$
$587$	20.9245			0.863648			0.431824	+	0.901958i	$0.357870\pi$
$588$		0			0
$589$	−15.3129			−0.630956
$590$		0			0
$591$	−0.178506	+	0.481898i	−0.00734277	+	0.0198226i
$592$		0			0
$593$	10.5845	−	18.3329i	0.434654	−	0.752842i	−0.562614	−	0.826720i	$-0.690204\pi$
$593$	10.5845	−	18.3329i	0.434654	−	0.752842i	0.997267	+	0.0738778i	$0.0235375\pi$
$594$		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	$-0.701174\pi$
$599$	−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	−0.395474	−	0.918477i	$-0.629420\pi$
$607$	−34.2123	−	19.7525i	−1.38864	−	0.801729i	−0.993162	+	0.116748i	$0.962753\pi$
$608$		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	0.683277	−	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	$0.0786952\pi$
$617$			12.1573i			0.489435i	−0.969594	+	0.244718i	$0.921305\pi$
$618$		0			0
$619$	16.8732	−	9.74173i	0.678190	−	0.391553i	−0.120983	−	0.992655i	$-0.538605\pi$
$619$	16.8732	−	9.74173i	0.678190	−	0.391553i	0.799173	+	0.601101i	$0.205271\pi$
$620$		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	$-0.285221\pi$
$631$	31.3846			1.24940			0.624701	+	0.780864i	$0.285221\pi$
$632$		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	−0.996502	−	0.0835697i	$-0.973368\pi$
$641$	−36.0118	+	20.7914i	−1.42238	+	0.821211i	−0.425878	+	0.904781i	$0.640035\pi$
$642$		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	0.994038	+	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
$651$	−3.93974	+	16.0223i	−0.154410	+	0.627963i
$652$		0			0
$653$	−18.3717	−	10.6069i	−0.718941	−	0.415081i	0.0954221	−	0.995437i	$-0.469580\pi$
$653$	−18.3717	−	10.6069i	−0.718941	−	0.415081i	−0.814363	+	0.580356i	$0.802913\pi$
$654$		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
$663$	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	−0.970886	−	0.239541i	$-0.923003\pi$
$677$	−7.23319	+	12.5283i	−0.277994	+	0.481500i	0.692892	+	0.721041i	$0.256336\pi$
$678$		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	$-0.453164\pi$
$683$	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	0.927861	−	0.372927i	$-0.121646\pi$
$691$	28.0961	+	16.2213i	1.06883	+	0.617087i	0.140966	+	0.990014i	$0.454979\pi$
$692$		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	$-0.805518\pi$
$701$		−	30.3777i		−	1.14735i	0.819084	−	0.573674i	$-0.194482\pi$
$702$		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	−0.380607	−	0.924737i	$-0.624285\pi$
$709$	16.2569	−	28.1578i	0.610542	−	1.05749i	0.991149	−	0.132753i	$-0.0423816\pi$
$710$		0			0
$711$	−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	$-0.896650\pi$
$719$	−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
$723$	−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	0.441045	−	0.897485i	$-0.354608\pi$
$733$	−3.13184	−	1.80817i	−0.115677	−	0.0667863i	−0.556722	+	0.830699i	$0.687941\pi$
$734$		0			0
$735$	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	−0.964232	−	0.265060i	$-0.914608\pi$
$739$	−19.3463	−	33.5087i	−0.711665	−	1.23264i	0.252567	−	0.967579i	$-0.418725\pi$
$740$		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	$-0.974823\pi$
$751$	−11.7841	+	20.4107i	−0.430009	+	0.744797i	0.566865	+	0.823811i	$0.308156\pi$
$752$		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	−0.999429	−	0.0337898i	$-0.989242\pi$
$761$	−12.9780	+	22.4785i	−0.470452	+	0.814846i	0.528977	+	0.848636i	$0.322576\pi$
$762$		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	$-0.768128\pi$
$769$		−	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	0.742842	−	0.669466i	$-0.233477\pi$
$773$	−5.79284	−	10.0335i	−0.208354	−	0.360879i	−0.951196	+	0.308587i	$0.900144\pi$
$774$		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	$-0.845732\pi$
$787$	−25.9153	+	14.9622i	−0.923779	+	0.533344i	−0.0389406	+	0.999242i	$0.512398\pi$
$788$		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	−0.461613	−	0.887081i	$-0.652729\pi$
$809$	2.15641	−	1.24501i	0.0758155	−	0.0437721i	0.537429	+	0.843309i	$0.319396\pi$
$810$		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	0.457721	−	0.889096i	$-0.348666\pi$
$821$	−2.38960	−	1.37963i	−0.0833975	−	0.0481495i	−0.541119	+	0.840946i	$0.681999\pi$
$822$		0			0
$823$	−14.2212	−	24.6318i	−0.495720	−	0.858612i	0.504268	−	0.863547i	$-0.331762\pi$
$823$	−14.2212	−	24.6318i	−0.495720	−	0.858612i	−0.999988	+	0.00493523i	$0.998429\pi$
$824$		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
$831$	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	$-0.426226\pi$
$839$	13.3067			0.459400			0.229700	+	0.973262i	$0.426226\pi$
$840$		0			0
$841$	−21.2383			−0.732354
$842$		0			0
$843$	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	$-0.740852\pi$
$853$		−	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	0.772794	−	0.634657i	$-0.218858\pi$
$857$	−4.77854	−	8.27667i	−0.163232	−	0.282726i	−0.936026	+	0.351931i	$0.885525\pi$
$858$		0			0
$859$	1.82940	+	1.05620i	0.0624183	+	0.0360372i	0.530884	−	0.847444i	$-0.321860\pi$
$859$	1.82940	+	1.05620i	0.0624183	+	0.0360372i	−0.468466	+	0.883481i	$0.655193\pi$
$860$		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	$-0.538472\pi$
$863$	−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
$873$	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	−0.689427	−	0.724355i	$-0.742138\pi$
$877$	8.36886	−	14.4953i	0.282596	−	0.489471i	0.972023	+	0.234884i	$0.0754709\pi$
$878$		0			0
$879$	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	$-0.417457\pi$
$883$	15.2392			0.512839			0.256419	+	0.966566i	$0.417457\pi$
$884$		0			0
$885$	2.64527	+	0.979870i	0.0889198	+	0.0329380i
$886$		0			0
$887$	28.0633	−	48.6071i	0.942275	−	1.63207i	0.181157	−	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
$891$	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	0.976139	+	0.217147i	$0.0696751\pi$
$907$	20.3625	+	35.2688i	0.676124	+	1.17108i	−0.300015	+	0.953935i	$0.596992\pi$
$908$		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	0.0405222	+	0.999179i	$0.487098\pi$
$919$	−25.6178	+	44.3713i	−0.845053	+	1.46367i	−0.885575	+	0.464496i	$0.846235\pi$
$920$		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	−0.833697	−	0.552223i	$-0.813780\pi$
$929$	1.87116	−	3.24094i	0.0613907	−	0.106332i	0.895087	+	0.445891i	$0.147113\pi$
$930$		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	$-0.983149\pi$
$937$		−	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	0.987911	−	0.155021i	$-0.0495446\pi$
$941$	11.0342	+	19.1117i	0.359703	+	0.623024i	−0.628208	+	0.778046i	$0.716211\pi$
$942$		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	$-0.132801\pi$
$947$	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	$-0.930015\pi$
$953$		−	13.4656i		−	0.436192i	0.975927	−	0.218096i	$-0.0699846\pi$
$954$		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	$-0.452433\pi$
$967$	9.25940			0.297762			0.148881	+	0.988855i	$0.452433\pi$
$968$		0			0
$969$	4.49535	−	12.1357i	0.144411	−	0.389855i
$970$		0			0
$971$	−19.9645	+	34.5795i	−0.640691	+	1.10971i	0.344587	+	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
$975$	17.3543	−	2.95838i	0.555781	−	0.0947439i
$976$		0			0
$977$	52.4299	−	30.2704i	1.67738	−	0.968436i	0.714060	−	0.700084i	$-0.246854\pi$
$977$	52.4299	−	30.2704i	1.67738	−	0.968436i	0.963321	−	0.268352i	$-0.0864791\pi$
$978$		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
$987$	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	$-0.00799146\pi$
$991$	15.0507	+	26.0686i	0.478102	+	0.828098i	−0.521583	+	0.853201i	$0.674658\pi$
$992$		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
$999$	30.4962	+	0.520289i	0.964858	+	0.0164612i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.u.a.17.5	✓	16	28.3	even	6
168.2.u.a.17.7	yes	16	84.59	odd	6
168.2.u.a.89.5	yes	16	12.11	even	2
168.2.u.a.89.7	yes	16	4.3	odd	2
336.2.bc.f.17.2		16	21.17	even	6	inner
336.2.bc.f.17.4		16	7.3	odd	6	inner
336.2.bc.f.257.2		16	1.1	even	1	trivial
336.2.bc.f.257.4		16	3.2	odd	2	inner
1176.2.k.a.881.3		16	84.47	odd	6
1176.2.k.a.881.4		16	28.23	odd	6
1176.2.k.a.881.13		16	28.19	even	6
1176.2.k.a.881.14		16	84.23	even	6
1176.2.u.b.521.2		16	84.11	even	6
1176.2.u.b.521.4		16	28.11	odd	6
1176.2.u.b.1097.2		16	28.27	even	2
1176.2.u.b.1097.4		16	84.83	odd	2
2352.2.k.i.881.3		16	21.2	odd	6
2352.2.k.i.881.4		16	7.5	odd	6
2352.2.k.i.881.13		16	7.2	even	3
2352.2.k.i.881.14		16	21.5	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bc (of order \(6\), degree \(2\), not 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

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Database

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