LMFDB - Embedded newform 336.2.bc.f.17.2

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			17.2
Root			$-0.601642 - 1.62420i$ of defining polynomial
Character	$\chi$	$=$	336.17
Dual form			336.2.bc.f.257.2

$q$-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 $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

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

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	0.881817	−	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	0.786499	−	0.617592i	$-0.211891\pi$
$11$	2.13889	+	1.23489i	0.644899	+	0.372332i	−0.141600	+	0.989924i	$0.545225\pi$
$12$		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	−0.0139720	−	0.999902i	$-0.504448\pi$
$19$	3.68319	−	2.12649i	0.844983	−	0.487851i	0.858955	+	0.512051i	$0.171114\pi$
$20$		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	$-0.311323\pi$
$23$	7.46351	−	4.30906i	1.55625	−	0.898501i	0.997610	−	0.0690910i	$-0.0220099\pi$
$24$		0			0
$25$	2.48944	−	4.31183i	0.497888	−	0.862367i
$26$		0			0
$27$	−2.52094	+	4.54366i	−0.485154	+	0.874429i
$28$		0			0
$29$			7.08790i			1.31619i	0.752935	+	0.658095i	$0.228637\pi$
$29$			7.08790i			1.31619i	−0.752935	+	0.658095i	$0.771363\pi$
$30$		0			0
$31$	−3.11812	−	1.80025i	−0.560031	−	0.323334i	0.193127	−	0.981174i	$-0.438137\pi$
$31$	−3.11812	−	1.80025i	−0.560031	−	0.323334i	−0.753158	+	0.657840i	$0.771470\pi$
$32$		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	$-0.252622\pi$
$43$	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	−0.975418	−	0.220364i	$-0.929276\pi$
$47$	−4.65190	−	8.05733i	−0.678549	−	1.17528i	0.296868	−	0.954918i	$-0.404058\pi$
$48$		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	$0.426889\pi$
$59$	−5.60299	+	9.70466i	−0.729447	+	1.26344i	−0.957117	+	0.289701i	$0.906444\pi$
$60$		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	−0.979328	−	0.202279i	$-0.935165\pi$
$67$	−2.57417	+	4.45860i	−0.314485	+	0.544705i	0.664843	+	0.746984i	$0.268499\pi$
$68$		0			0
$69$	−9.52973	+	11.4891i	−1.14724	+	1.38313i
$70$		0			0
$71$			7.79323i			0.924886i	0.886649	+	0.462443i	$0.153027\pi$
$71$			7.79323i			0.924886i	−0.886649	+	0.462443i	$0.846973\pi$
$72$		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	0.659012	−	0.752133i	$-0.270975\pi$
$79$	−2.86075	−	4.95497i	−0.321860	−	0.557478i	−0.980872	+	0.194655i	$0.937641\pi$
$80$		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	0.998976	−	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	−0.492724	−	0.870186i	$-0.663999\pi$
$103$	0.147333	−	0.0850626i	0.0145171	−	0.00838147i	0.507241	+	0.861804i	$0.330665\pi$
$104$		0			0
$105$	−0.185654	+	0.639626i	−0.0181179	+	0.0624211i
$106$		0			0
$107$	6.03900	−	3.48662i	0.583813	−	0.337064i	−0.178835	−	0.983879i	$-0.557233\pi$
$107$	6.03900	−	3.48662i	0.583813	−	0.337064i	0.762647	+	0.646815i	$0.223899\pi$
$108$		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	$-0.394503\pi$
$127$	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	0.967912	−	0.251289i	$-0.0808545\pi$
$131$	3.04832	+	5.27985i	0.266333	+	0.461303i	−0.701579	+	0.712592i	$0.747521\pi$
$132$		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	$0.00158880\pi$
$139$			0.117694i			0.00998266i	−0.999988	+	0.00499133i	$0.998411\pi$
$140$		0			0
$141$	12.4032	+	10.2879i	1.04454	+	0.866401i
$142$		0			0
$143$	2.52094	−	4.36639i	0.210811	−	0.365136i
$144$		0			0
$145$	−0.892131	+	0.515072i	−0.0740875	+	0.0427744i
$146$		0			0
$147$	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	−0.916414	−	0.400232i	$-0.868930\pi$
$151$	−1.37132	+	2.37519i	−0.111596	+	0.193290i	0.804818	+	0.593522i	$0.202263\pi$
$152$		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	0.775793	−	0.630987i	$-0.217350\pi$
$163$	−2.02428	−	3.50616i	−0.158554	−	0.274624i	−0.934347	+	0.356363i	$0.884017\pi$
$164$		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	0.877263	+	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	0.614309	−	0.789065i	$-0.289435\pi$
$179$	3.18574	+	1.83929i	0.238113	+	0.137475i	−0.376196	+	0.926540i	$0.622768\pi$
$180$		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	−0.534730	−	0.845023i	$-0.679587\pi$
$191$	−0.971326	+	0.560795i	−0.0702827	+	0.0405777i	0.464447	+	0.885601i	$0.346253\pi$
$192$		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	$0.0877962\pi$
$199$	23.6874	+	13.6759i	1.67915	+	0.969460i	0.716951	+	0.697124i	$0.245537\pi$
$200$		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	$0.0741487\pi$
$223$			6.89447i			0.461688i	−0.972991	+	0.230844i	$0.925851\pi$
$224$		0			0
$225$	−2.76084	−	14.6793i	−0.184056	−	0.978617i
$226$		0			0
$227$	6.70734	−	11.6174i	0.445182	−	0.771077i	−0.552883	−	0.833259i	$-0.686472\pi$
$227$	6.70734	−	11.6174i	0.445182	−	0.771077i	0.998065	+	0.0621816i	$0.0198058\pi$
$228$		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	$0.189956\pi$
$239$			17.3756i			1.12394i	−0.827159	+	0.561968i	$0.810044\pi$
$240$		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	$-0.535210\pi$
$251$	−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	0.502976	−	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	0.0649777	−	0.997887i	$-0.479302\pi$
$263$	−12.4343	−	7.17892i	−0.766729	−	0.442671i	−0.831706	+	0.555216i	$0.812636\pi$
$264$		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	−0.792015	−	0.610501i	$-0.790968\pi$
$271$	−10.8537	+	6.26636i	−0.659313	+	0.380654i	0.132702	+	0.991156i	$0.457635\pi$
$272$		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	0.534855	−	0.844944i	$-0.320366\pi$
$283$	1.18666	+	0.685120i	0.0705397	+	0.0407261i	−0.464315	+	0.885670i	$0.653700\pi$
$284$		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	$-0.796566\pi$
$307$		−	20.9023i		−	1.19296i	0.802629	−	0.596479i	$-0.203434\pi$
$308$		0			0
$309$	−0.188121	+	0.226800i	−0.0107018	+	0.0129022i
$310$		0			0
$311$	−5.74040	+	9.94267i	−0.325508	+	0.563797i	−0.981615	−	0.190871i	$-0.938869\pi$
$311$	−5.74040	+	9.94267i	−0.325508	+	0.563797i	0.656107	+	0.754668i	$0.272202\pi$
$312$		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	0.994303	−	0.106595i	$-0.0339948\pi$
$331$	7.36537	+	12.7572i	0.404837	+	0.701199i	−0.589465	+	0.807794i	$0.700661\pi$
$332$		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	0.0570320	−	0.998372i	$-0.481836\pi$
$347$	−14.5124	−	8.37875i	−0.779068	−	0.449795i	−0.836100	+	0.548577i	$0.815170\pi$
$348$		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	−0.636357	−	0.771395i	$-0.719559\pi$
$359$	−5.42817	+	3.13395i	−0.286488	+	0.165404i	0.349869	+	0.936799i	$0.386226\pi$
$360$		0			0
$361$	−0.456052	+	0.789905i	−0.0240027	+	0.0415739i
$362$		0			0
$363$	6.53266	+	5.41855i	0.342876	+	0.284400i
$364$		0			0
$365$			1.89662i			0.0992734i
$366$		0			0
$367$	14.5823	+	8.41907i	0.761188	+	0.439472i	0.829722	−	0.558177i	$-0.188499\pi$
$367$	14.5823	+	8.41907i	0.761188	+	0.439472i	−0.0685342	+	0.997649i	$0.521832\pi$
$368$		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	$-0.379505\pi$
$379$	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	0.711086	−	0.703105i	$-0.248204\pi$
$383$	−4.95842	−	8.58824i	−0.253364	−	0.438839i	−0.964450	+	0.264266i	$0.914870\pi$
$384$		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	$-0.262975\pi$
$419$	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	0.812624	−	0.582788i	$-0.198038\pi$
$431$	14.8277	+	8.56080i	0.714227	+	0.412359i	−0.0983974	+	0.995147i	$0.531372\pi$
$432$		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	0.0271602	−	0.999631i	$-0.491354\pi$
$439$	18.9922	−	10.9651i	0.906446	−	0.523337i	0.879286	+	0.476294i	$0.158020\pi$
$440$		0			0
$441$	−0.868806	+	20.9820i	−0.0413717	+	0.999144i
$442$		0			0
$443$	−17.7589	+	10.2531i	−0.843750	+	0.487139i	−0.858537	−	0.512752i	$-0.828626\pi$
$443$	−17.7589	+	10.2531i	−0.843750	+	0.487139i	0.0147873	+	0.999891i	$0.495293\pi$
$444$		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	$-0.588662\pi$
$463$	−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	0.919577	−	0.392910i	$-0.128531\pi$
$467$	2.58282	+	4.47358i	0.119519	+	0.207013i	−0.800058	+	0.599922i	$0.795198\pi$
$468$		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	−0.998403	−	0.0564848i	$-0.982011\pi$
$479$	−9.85496	+	17.0693i	−0.450284	+	0.779915i	0.548119	+	0.836400i	$0.315344\pi$
$480$		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	−0.917159	−	0.398522i	$-0.869523\pi$
$487$	−2.50360	+	4.33637i	−0.113449	+	0.196500i	0.803710	+	0.595022i	$0.202857\pi$
$488$		0			0
$489$	5.39730	+	4.47682i	0.244074	+	0.202449i
$490$		0			0
$491$			3.55902i			0.160616i	0.996770	+	0.0803081i	$0.0255904\pi$
$491$			3.55902i			0.160616i	−0.996770	+	0.0803081i	$0.974410\pi$
$492$		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	0.856825	−	0.515608i	$-0.172434\pi$
$499$	−0.404702	−	0.700965i	−0.0181170	−	0.0313795i	−0.874942	+	0.484228i	$0.839100\pi$
$500$		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	0.726087	−	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	0.127912	−	0.991785i	$-0.459172\pi$
$523$	24.0305	−	13.8740i	1.05078	−	0.606668i	0.922868	+	0.385117i	$0.125839\pi$
$524$		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	$-0.612133\pi$
$547$	−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	−0.370753	−	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	−0.982225	−	0.187705i	$-0.939895\pi$
$563$	−7.79584	+	13.5028i	−0.328556	+	0.569075i	0.653670	+	0.756780i	$0.273228\pi$
$564$		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	−0.801135	−	0.598484i	$-0.795770\pi$
$571$	2.81334	−	4.87284i	0.117735	−	0.203922i	0.918870	+	0.394561i	$0.129103\pi$
$572$		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	$-0.357870\pi$
$587$	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	0.997267	−	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	0.403366	−	0.915039i	$-0.367840\pi$
$599$	−4.58648	−	2.64801i	−0.187399	−	0.108195i	−0.590764	+	0.806844i	$0.701174\pi$
$600$		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	−0.993162	−	0.116748i	$-0.962753\pi$
$607$	−34.2123	+	19.7525i	−1.38864	+	0.801729i	−0.395474	+	0.918477i	$0.629420\pi$
$608$		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	0.799173	−	0.601101i	$-0.205271\pi$
$619$	16.8732	+	9.74173i	0.678190	+	0.391553i	−0.120983	+	0.992655i	$0.538605\pi$
$620$		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	−0.425878	−	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	$0.0859549\pi$
$643$			13.5290i			0.533531i	−0.963761	+	0.266766i	$0.914045\pi$
$644$		0			0
$645$	−1.78196	−	1.47806i	−0.0701646	−	0.0581984i
$646$		0			0
$647$	15.0442	−	26.0573i	0.591449	−	1.02442i	−0.402589	−	0.915381i	$-0.631890\pi$
$647$	15.0442	−	26.0573i	0.591449	−	1.02442i	0.994038	−	0.109038i	$-0.0347771\pi$
$648$		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	$-0.983382\pi$
$659$		−	2.67926i		−	0.104369i	0.998637	−	0.0521846i	$-0.0166184\pi$
$660$		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	0.929972	−	0.367630i	$-0.119831\pi$
$683$	28.1356	+	16.2441i	1.07658	+	0.621564i	0.146609	+	0.989195i	$0.453164\pi$
$684$		0			0
$685$			2.91730i			0.111464i
$686$		0			0
$687$	7.03555	−	8.48214i	0.268423	−	0.323614i
$688$		0			0
$689$	−5.29882	+	9.17783i	−0.201869	+	0.349647i
$690$		0			0
$691$	28.0961	−	16.2213i	1.06883	−	0.617087i	0.140966	−	0.990014i	$-0.454979\pi$
$691$	28.0961	−	16.2213i	1.06883	−	0.617087i	0.927861	+	0.372927i	$0.121646\pi$
$692$		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	0.750145	−	0.661273i	$-0.229984\pi$
$719$	−5.29867	−	9.17757i	−0.197607	−	0.342266i	−0.947752	+	0.319008i	$0.896650\pi$
$720$		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	$0.197549\pi$
$727$			31.3600i			1.16308i	−0.813518	+	0.581540i	$0.802451\pi$
$728$		0			0
$729$	−14.2898	−	22.9086i	−0.529251	−	0.848466i
$730$		0			0
$731$	8.07874	−	13.9928i	0.298803	−	0.517542i
$732$		0			0
$733$	−3.13184	+	1.80817i	−0.115677	+	0.0667863i	−0.556722	−	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	$0.418725\pi$
$739$	−19.3463	+	33.5087i	−0.711665	+	1.23264i	−0.964232	+	0.265060i	$0.914608\pi$
$740$		0			0
$741$	11.5745	+	9.60056i	0.425201	+	0.352685i
$742$		0			0
$743$		−	45.1194i		−	1.65527i	−0.561266	−	0.827635i	$-0.689686\pi$
$743$		−	45.1194i		−	1.65527i	0.561266	−	0.827635i	$-0.310314\pi$
$744$		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	0.566865	−	0.823811i	$-0.308156\pi$
$751$	−11.7841	−	20.4107i	−0.430009	−	0.744797i	−0.996874	+	0.0790136i	$0.974823\pi$
$752$		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	−0.0389406	−	0.999242i	$-0.512398\pi$
$787$	−25.9153	−	14.9622i	−0.923779	−	0.533344i	−0.884839	+	0.465897i	$0.845732\pi$
$788$		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	$-0.909455\pi$
$811$		−	15.9838i		−	0.561269i	0.959815	−	0.280634i	$-0.0905448\pi$
$812$		0			0
$813$	13.8584	−	16.7078i	0.486036	−	0.585970i
$814$		0			0
$815$	0.294206	−	0.509581i	0.0103056	−	0.0178498i
$816$		0			0
$817$	33.8740	−	19.5572i	1.18510	−	0.684219i
$818$		0			0
$819$	−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	−0.999988	−	0.00493523i	$-0.998429\pi$
$823$	−14.2212	+	24.6318i	−0.495720	+	0.858612i	0.504268	+	0.863547i	$0.331762\pi$
$824$		0			0
$825$	−13.5974	+	16.3932i	−0.473401	+	0.570738i
$826$		0			0
$827$			30.6070i			1.06431i	0.846647	+	0.532154i	$0.178617\pi$
$827$			30.6070i			1.06431i	−0.846647	+	0.532154i	$0.821383\pi$
$828$		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	$-0.426226\pi$
$839$	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	$0.259148\pi$
$853$			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	−0.468466	−	0.883481i	$-0.655193\pi$
$859$	1.82940	−	1.05620i	0.0624183	−	0.0360372i	0.530884	+	0.847444i	$0.321860\pi$
$860$		0			0
$861$	−16.9182	−	17.6333i	−0.576571	−	0.600940i
$862$		0			0
$863$	−30.5684	+	17.6487i	−1.04056	+	0.600768i	−0.919992	−	0.391936i	$-0.871805\pi$
$863$	−30.5684	+	17.6487i	−1.04056	+	0.600768i	−0.120569	+	0.992705i	$0.538472\pi$
$864$		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	$-0.417457\pi$
$883$	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	0.761118	+	0.648613i	$0.224651\pi$
$887$	28.0633	+	48.6071i	0.942275	+	1.63207i	0.181157	+	0.983454i	$0.442016\pi$
$888$		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	$-0.596992\pi$
$907$	20.3625	−	35.2688i	0.676124	−	1.17108i	0.976139	−	0.217147i	$-0.0696751\pi$
$908$		0			0
$909$	−8.94266	−	47.5478i	−0.296609	−	1.57706i
$910$		0			0
$911$			31.0308i			1.02810i	0.857761	+	0.514049i	$0.171855\pi$
$911$			31.0308i			1.02810i	−0.857761	+	0.514049i	$0.828145\pi$
$912$		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	$-0.846235\pi$
$919$	−25.6178	−	44.3713i	−0.845053	−	1.46367i	0.0405222	−	0.999179i	$-0.487098\pi$
$920$		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	0.106191	−	0.994346i	$-0.466134\pi$
$947$	31.4016	−	18.1297i	1.02042	−	0.589137i	0.914224	+	0.405208i	$0.132801\pi$
$948$		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	$-0.452433\pi$
$967$	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	−0.985279	−	0.170956i	$-0.945314\pi$
$971$	−19.9645	−	34.5795i	−0.640691	−	1.10971i	0.344587	−	0.938754i	$-0.388019\pi$
$972$		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	$-0.617036\pi$
$983$	19.7027	−	34.1261i	0.628419	−	1.08845i	0.987869	−	0.155289i	$-0.0496308\pi$
$984$		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	−0.521583	−	0.853201i	$-0.674658\pi$
$991$	15.0507	−	26.0686i	0.478102	−	0.828098i	0.999685	+	0.0251033i	$0.00799146\pi$
$992$		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	336.2.bc.f.17.2		16
3.2	odd	2	inner	336.2.bc.f.17.4		16
4.3	odd	2		168.2.u.a.17.7	yes	16
7.3	odd	6		2352.2.k.i.881.3		16
7.4	even	3		2352.2.k.i.881.14		16
7.5	odd	6	inner	336.2.bc.f.257.4		16
12.11	even	2		168.2.u.a.17.5	✓	16
21.5	even	6	inner	336.2.bc.f.257.2		16
21.11	odd	6		2352.2.k.i.881.4		16
21.17	even	6		2352.2.k.i.881.13		16
28.3	even	6		1176.2.k.a.881.14		16
28.11	odd	6		1176.2.k.a.881.3		16
28.19	even	6		168.2.u.a.89.5	yes	16
28.23	odd	6		1176.2.u.b.1097.4		16
28.27	even	2		1176.2.u.b.521.2		16
84.11	even	6		1176.2.k.a.881.13		16
84.23	even	6		1176.2.u.b.1097.2		16
84.47	odd	6		168.2.u.a.89.7	yes	16
84.59	odd	6		1176.2.k.a.881.4		16
84.83	odd	2		1176.2.u.b.521.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.u.a.17.5	✓	16	12.11	even	2
168.2.u.a.17.7	yes	16	4.3	odd	2
168.2.u.a.89.5	yes	16	28.19	even	6
168.2.u.a.89.7	yes	16	84.47	odd	6
336.2.bc.f.17.2		16	1.1	even	1	trivial
336.2.bc.f.17.4		16	3.2	odd	2	inner
336.2.bc.f.257.2		16	21.5	even	6	inner
336.2.bc.f.257.4		16	7.5	odd	6	inner
1176.2.k.a.881.3		16	28.11	odd	6
1176.2.k.a.881.4		16	84.59	odd	6
1176.2.k.a.881.13		16	84.11	even	6
1176.2.k.a.881.14		16	28.3	even	6
1176.2.u.b.521.2		16	28.27	even	2
1176.2.u.b.521.4		16	84.83	odd	2
1176.2.u.b.1097.2		16	84.23	even	6
1176.2.u.b.1097.4		16	28.23	odd	6
2352.2.k.i.881.3		16	7.3	odd	6
2352.2.k.i.881.4		16	21.11	odd	6
2352.2.k.i.881.13		16	21.17	even	6
2352.2.k.i.881.14		16	7.4	even	3

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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