LMFDB - Embedded newform 136.2.n.c.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,2,Mod(9,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("136.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	136.n (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.08596546749$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 28x^{10} + 258x^{8} + 880x^{6} + 1033x^{4} + 132x^{2} + 4 $ x^12 + 28x^10 + 258x^8 + 880x^6 + 1033x^4 + 132*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			49.1
Root			$1.75800i$ of defining polynomial
Character	$\chi$	$=$	136.49
Dual form			136.2.n.c.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.24310 - 3.00110i) q^{3} +(0.194339 - 0.0804980i) q^{5} +(-1.76317 - 0.730328i) q^{7} +(-5.33998 + 5.33998i) q^{9} +O(q^{10})$	\(q+(-1.24310 - 3.00110i) q^{3} +(0.194339 - 0.0804980i) q^{5} +(-1.76317 - 0.730328i) q^{7} +(-5.33998 + 5.33998i) q^{9} +(0.356936 - 0.861721i) q^{11} -5.90040i q^{13} +(-0.483165 - 0.483165i) q^{15} +(4.07521 - 0.626609i) q^{17} +(3.51903 + 3.51903i) q^{19} +6.19930i q^{21} +(1.71673 - 4.14454i) q^{23} +(-3.50425 + 3.50425i) q^{25} +(13.6606 + 5.65841i) q^{27} +(6.46407 - 2.67750i) q^{29} +(-1.31309 - 3.17008i) q^{31} -3.02981 q^{33} -0.401443 q^{35} +(-1.21987 - 2.94504i) q^{37} +(-17.7077 + 7.33476i) q^{39} +(7.03058 + 2.91216i) q^{41} +(-2.78354 + 2.78354i) q^{43} +(-0.607910 + 1.46763i) q^{45} +9.54449i q^{47} +(-2.37437 - 2.37437i) q^{49} +(-6.94639 - 11.4512i) q^{51} +(2.21135 + 2.21135i) q^{53} -0.196199i q^{55} +(6.18646 - 14.9354i) q^{57} +(1.95511 - 1.95511i) q^{59} +(-0.440083 - 0.182288i) q^{61} +(13.3152 - 5.51534i) q^{63} +(-0.474971 - 1.14668i) q^{65} -4.33796 q^{67} -14.5722 q^{69} +(-0.788702 - 1.90409i) q^{71} +(0.971614 - 0.402456i) q^{73} +(14.8727 + 6.16047i) q^{75} +(-1.25868 + 1.25868i) q^{77} +(-4.85539 + 11.7219i) q^{79} -25.3751i q^{81} +(0.666789 + 0.666789i) q^{83} +(0.741534 - 0.449821i) q^{85} +(-16.0709 - 16.0709i) q^{87} +3.51138i q^{89} +(-4.30923 + 10.4034i) q^{91} +(-7.88141 + 7.88141i) q^{93} +(0.967161 + 0.400611i) q^{95} +(-2.66222 + 1.10273i) q^{97} +(2.69554 + 6.50760i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{5} - 8 q^{9}+O(q^{10}) $ 12 * q + 4 * q^5 - 8 * q^9	$ 12 q + 4 q^{5} - 8 q^{9} - 12 q^{11} + 20 q^{15} + 4 q^{17} - 4 q^{19} - 8 q^{23} - 16 q^{25} + 24 q^{27} + 8 q^{29} - 32 q^{31} - 24 q^{33} - 32 q^{35} + 4 q^{37} - 8 q^{39} + 16 q^{41} + 8 q^{43} - 64 q^{45} + 44 q^{49} - 8 q^{51} - 8 q^{53} - 12 q^{57} + 16 q^{59} + 44 q^{61} + 100 q^{63} - 20 q^{65} - 40 q^{67} + 56 q^{69} + 32 q^{71} + 8 q^{73} + 92 q^{75} - 12 q^{77} - 8 q^{79} + 40 q^{83} + 40 q^{85} - 84 q^{87} - 40 q^{91} - 76 q^{93} + 28 q^{95} - 16 q^{97} - 68 q^{99}+O(q^{100}) $ 12 * q + 4 * q^5 - 8 * q^9 - 12 * q^11 + 20 * q^15 + 4 * q^17 - 4 * q^19 - 8 * q^23 - 16 * q^25 + 24 * q^27 + 8 * q^29 - 32 * q^31 - 24 * q^33 - 32 * q^35 + 4 * q^37 - 8 * q^39 + 16 * q^41 + 8 * q^43 - 64 * q^45 + 44 * q^49 - 8 * q^51 - 8 * q^53 - 12 * q^57 + 16 * q^59 + 44 * q^61 + 100 * q^63 - 20 * q^65 - 40 * q^67 + 56 * q^69 + 32 * q^71 + 8 * q^73 + 92 * q^75 - 12 * q^77 - 8 * q^79 + 40 * q^83 + 40 * q^85 - 84 * q^87 - 40 * q^91 - 76 * q^93 + 28 * q^95 - 16 * q^97 - 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{8}\right)$

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
$3$	−1.24310	−	3.00110i	−0.717701	−	1.73268i	−0.679794	−	0.733403i	$-0.737931\pi$
$3$	−1.24310	−	3.00110i	−0.717701	−	1.73268i	−0.0379071	−	0.999281i	$-0.512069\pi$
$4$		0			0
$5$	0.194339	−	0.0804980i	0.0869112	−	0.0359998i	−0.338804	−	0.940857i	$-0.610022\pi$
$5$	0.194339	−	0.0804980i	0.0869112	−	0.0359998i	0.425715	+	0.904857i	$0.360022\pi$
$6$		0			0
$7$	−1.76317	−	0.730328i	−0.666414	−	0.276038i	0.0237205	−	0.999719i	$-0.492449\pi$
$7$	−1.76317	−	0.730328i	−0.666414	−	0.276038i	−0.690135	+	0.723681i	$0.742449\pi$
$8$		0			0
$9$	−5.33998	+	5.33998i	−1.77999	+	1.77999i
$10$		0			0
$11$	0.356936	−	0.861721i	0.107620	−	0.259819i	−0.860890	−	0.508791i	$-0.830093\pi$
$11$	0.356936	−	0.861721i	0.107620	−	0.259819i	0.968511	+	0.248972i	$0.0800927\pi$
$12$		0			0
$13$		−	5.90040i		−	1.63648i	−0.574879	−	0.818239i	$-0.694951\pi$
$13$		−	5.90040i		−	1.63648i	0.574879	−	0.818239i	$-0.305049\pi$
$14$		0			0
$15$	−0.483165	−	0.483165i	−0.124753	−	0.124753i
$16$		0			0
$17$	4.07521	−	0.626609i	0.988384	−	0.151975i
$17$	4.07521	−	0.626609i	0.988384	−	0.151975i
$18$		0			0
$19$	3.51903	+	3.51903i	0.807321	+	0.807321i	0.984228	−	0.176907i	$-0.0566091\pi$
$19$	3.51903	+	3.51903i	0.807321	+	0.807321i	−0.176907	+	0.984228i	$0.556609\pi$
$20$		0			0
$21$			6.19930i			1.35280i
$22$		0			0
$23$	1.71673	−	4.14454i	0.357962	−	0.864197i	−0.637624	−	0.770347i	$-0.720083\pi$
$23$	1.71673	−	4.14454i	0.357962	−	0.864197i	0.995586	−	0.0938492i	$-0.0299172\pi$
$24$		0			0
$25$	−3.50425	+	3.50425i	−0.700849	+	0.700849i
$26$		0			0
$27$	13.6606	+	5.65841i	2.62898	+	1.08896i
$28$		0			0
$29$	6.46407	−	2.67750i	1.20035	−	0.497200i	0.309236	−	0.950985i	$-0.399927\pi$
$29$	6.46407	−	2.67750i	1.20035	−	0.497200i	0.891111	+	0.453785i	$0.149927\pi$
$30$		0			0
$31$	−1.31309	−	3.17008i	−0.235838	−	0.569362i	0.761007	−	0.648744i	$-0.224705\pi$
$31$	−1.31309	−	3.17008i	−0.235838	−	0.569362i	−0.996844	+	0.0793816i	$0.974705\pi$
$32$		0			0
$33$	−3.02981			−0.527423
$34$		0			0
$35$	−0.401443			−0.0678562
$36$		0			0
$37$	−1.21987	−	2.94504i	−0.200546	−	0.484161i	0.791327	−	0.611393i	$-0.209391\pi$
$37$	−1.21987	−	2.94504i	−0.200546	−	0.484161i	−0.991873	+	0.127232i	$0.959391\pi$
$38$		0			0
$39$	−17.7077	+	7.33476i	−2.83550	+	1.17450i
$40$		0			0
$41$	7.03058	+	2.91216i	1.09799	+	0.454803i	0.856787	−	0.515671i	$-0.172457\pi$
$41$	7.03058	+	2.91216i	1.09799	+	0.454803i	0.241205	+	0.970474i	$0.422457\pi$
$42$		0			0
$43$	−2.78354	+	2.78354i	−0.424485	+	0.424485i	−0.886745	−	0.462259i	$-0.847039\pi$
$43$	−2.78354	+	2.78354i	−0.424485	+	0.424485i	0.462259	+	0.886745i	$0.347039\pi$
$44$		0			0
$45$	−0.607910	+	1.46763i	−0.0906219	+	0.218781i
$46$		0			0
$47$			9.54449i			1.39221i	0.717941	+	0.696104i	$0.245085\pi$
$47$			9.54449i			1.39221i	−0.717941	+	0.696104i	$0.754915\pi$
$48$		0			0
$49$	−2.37437	−	2.37437i	−0.339195	−	0.339195i
$50$		0			0
$51$	−6.94639	−	11.4512i	−0.972689	−	1.60349i
$52$		0			0
$53$	2.21135	+	2.21135i	0.303753	+	0.303753i	0.842480	−	0.538727i	$-0.181095\pi$
$53$	2.21135	+	2.21135i	0.303753	+	0.303753i	−0.538727	+	0.842480i	$0.681095\pi$
$54$		0			0
$55$		−	0.196199i		−	0.0264555i
$56$		0			0
$57$	6.18646	−	14.9354i	0.819417	−	1.97825i
$58$		0			0
$59$	1.95511	−	1.95511i	0.254534	−	0.254534i	−0.568293	−	0.822826i	$-0.692396\pi$
$59$	1.95511	−	1.95511i	0.254534	−	0.254534i	0.822826	+	0.568293i	$0.192396\pi$
$60$		0			0
$61$	−0.440083	−	0.182288i	−0.0563468	−	0.0233396i	0.354332	−	0.935120i	$-0.384708\pi$
$61$	−0.440083	−	0.182288i	−0.0563468	−	0.0233396i	−0.410679	+	0.911780i	$0.634708\pi$
$62$		0			0
$63$	13.3152	−	5.51534i	1.67756	−	0.694867i
$64$		0			0
$65$	−0.474971	−	1.14668i	−0.0589129	−	0.142228i
$66$		0			0
$67$	−4.33796			−0.529966			−0.264983	−	0.964253i	$-0.585366\pi$
$67$	−4.33796			−0.529966			−0.264983	+	0.964253i	$0.585366\pi$
$68$		0			0
$69$	−14.5722			−1.75429
$70$		0			0
$71$	−0.788702	−	1.90409i	−0.0936017	−	0.225974i	0.870144	−	0.492798i	$-0.164026\pi$
$71$	−0.788702	−	1.90409i	−0.0936017	−	0.225974i	−0.963745	+	0.266824i	$0.914026\pi$
$72$		0			0
$73$	0.971614	−	0.402456i	0.113719	−	0.0471039i	−0.325099	−	0.945680i	$-0.605397\pi$
$73$	0.971614	−	0.402456i	0.113719	−	0.0471039i	0.438817	+	0.898576i	$0.355397\pi$
$74$		0			0
$75$	14.8727	+	6.16047i	1.71735	+	0.711350i
$76$		0			0
$77$	−1.25868	+	1.25868i	−0.143440	+	0.143440i
$78$		0			0
$79$	−4.85539	+	11.7219i	−0.546274	+	1.31882i	0.373957	+	0.927446i	$0.378001\pi$
$79$	−4.85539	+	11.7219i	−0.546274	+	1.31882i	−0.920231	+	0.391376i	$0.871999\pi$
$80$		0			0
$81$		−	25.3751i		−	2.81946i
$82$		0			0
$83$	0.666789	+	0.666789i	0.0731895	+	0.0731895i	0.742754	−	0.669564i	$-0.233519\pi$
$83$	0.666789	+	0.666789i	0.0731895	+	0.0731895i	−0.669564	+	0.742754i	$0.733519\pi$
$84$		0			0
$85$	0.741534	−	0.449821i	0.0804306	−	0.0487900i
$86$		0			0
$87$	−16.0709	−	16.0709i	−1.72298	−	1.72298i
$88$		0			0
$89$			3.51138i			0.372205i	0.982530	+	0.186103i	$0.0595857\pi$
$89$			3.51138i			0.372205i	−0.982530	+	0.186103i	$0.940414\pi$
$90$		0			0
$91$	−4.30923	+	10.4034i	−0.451730	+	1.09057i
$92$		0			0
$93$	−7.88141	+	7.88141i	−0.817264	+	0.817264i
$94$		0			0
$95$	0.967161	+	0.400611i	0.0992286	+	0.0411018i
$96$		0			0
$97$	−2.66222	+	1.10273i	−0.270307	+	0.111965i	−0.513720	−	0.857958i	$-0.671733\pi$
$97$	−2.66222	+	1.10273i	−0.270307	+	0.111965i	0.243413	+	0.969923i	$0.421733\pi$
$98$		0			0
$99$	2.69554	+	6.50760i	0.270912	+	0.654039i
$100$		0			0
$101$	−1.78366			−0.177480			−0.0887402	−	0.996055i	$-0.528284\pi$
$101$	−1.78366			−0.177480			−0.0887402	+	0.996055i	$0.528284\pi$
$102$		0			0
$103$	12.3264			1.21455			0.607277	−	0.794490i	$-0.292262\pi$
$103$	12.3264			1.21455			0.607277	+	0.794490i	$0.292262\pi$
$104$		0			0
$105$	0.499031	+	1.20477i	0.0487005	+	0.117573i
$106$		0			0
$107$	8.12901	−	3.36715i	0.785861	−	0.325514i	0.0465831	−	0.998914i	$-0.485167\pi$
$107$	8.12901	−	3.36715i	0.785861	−	0.325514i	0.739278	+	0.673400i	$0.235167\pi$
$108$		0			0
$109$	−17.0375	−	7.05716i	−1.63190	−	0.675953i	−0.636452	−	0.771316i	$-0.719599\pi$
$109$	−17.0375	−	7.05716i	−1.63190	−	0.675953i	−0.995443	+	0.0953629i	$0.969599\pi$
$110$		0			0
$111$	−7.32192	+	7.32192i	−0.694966	+	0.694966i
$112$		0			0
$113$	−5.53342	+	13.3589i	−0.520540	+	1.25669i	0.417028	+	0.908894i	$0.363072\pi$
$113$	−5.53342	+	13.3589i	−0.520540	+	1.25669i	−0.937568	+	0.347801i	$0.886928\pi$
$114$		0			0
$115$		−	0.943640i		−	0.0879949i
$116$		0			0
$117$	31.5080	+	31.5080i	2.91292	+	2.91292i
$118$		0			0
$119$	−7.64291	−	1.87142i	−0.700624	−	0.171553i
$120$		0			0
$121$	7.16302	+	7.16302i	0.651183	+	0.651183i
$122$		0			0
$123$		−	24.7195i		−	2.22889i
$124$		0			0
$125$	−0.801418	+	1.93479i	−0.0716810	+	0.173053i
$126$		0			0
$127$	11.2096	−	11.2096i	0.994688	−	0.994688i	−0.00529822	−	0.999986i	$-0.501686\pi$
$127$	11.2096	−	11.2096i	0.994688	−	0.994688i	0.999986	+	0.00529822i	$0.00168649\pi$
$128$		0			0
$129$	11.8139	+	4.89346i	1.04015	+	0.430845i
$130$		0			0
$131$	−2.21975	+	0.919452i	−0.193941	+	0.0803329i	−0.477540	−	0.878610i	$-0.658471\pi$
$131$	−2.21975	+	0.919452i	−0.193941	+	0.0803329i	0.283599	+	0.958943i	$0.408471\pi$
$132$		0			0
$133$	−3.63459	−	8.77468i	−0.315159	−	0.760861i
$134$		0			0
$135$	3.11028			0.267690
$136$		0			0
$137$	12.7319			1.08776			0.543881	−	0.839162i	$-0.316954\pi$
$137$	12.7319			1.08776			0.543881	+	0.839162i	$0.316954\pi$
$138$		0			0
$139$	1.25805	+	3.03721i	0.106707	+	0.257613i	0.968210	−	0.250140i	$-0.0804765\pi$
$139$	1.25805	+	3.03721i	0.106707	+	0.257613i	−0.861503	+	0.507752i	$0.830477\pi$
$140$		0			0
$141$	28.6440	−	11.8647i	2.41226	−	0.999189i
$142$		0			0
$143$	−5.08450	−	2.10607i	−0.425187	−	0.176118i
$144$		0			0
$145$	1.04069	−	1.04069i	0.0864245	−	0.0864245i
$146$		0			0
$147$	−4.17414	+	10.0773i	−0.344278	+	0.831160i
$148$		0			0
$149$		−	2.25321i		−	0.184590i	−0.995732	−	0.0922951i	$-0.970580\pi$
$149$		−	2.25321i		−	0.184590i	0.995732	−	0.0922951i	$-0.0294203\pi$
$150$		0			0
$151$	12.3393	+	12.3393i	1.00416	+	1.00416i	0.999991	+	0.00416836i	$0.00132683\pi$
$151$	12.3393	+	12.3393i	1.00416	+	1.00416i	0.00416836	+	0.999991i	$0.498673\pi$
$152$		0			0
$153$	−18.4155	+	25.1076i	−1.48880	+	2.02983i
$154$		0			0
$155$	−0.510370	−	0.510370i	−0.0409939	−	0.0409939i
$156$		0			0
$157$			2.52901i			0.201837i	0.994895	+	0.100919i	$0.0321782\pi$
$157$			2.52901i			0.201837i	−0.994895	+	0.100919i	$0.967822\pi$
$158$		0			0
$159$	3.88756	−	9.38541i	0.308304	−	0.744311i
$160$		0			0
$161$	−6.05375	+	6.05375i	−0.477102	+	0.477102i
$162$		0			0
$163$	−8.55843	−	3.54502i	−0.670348	−	0.277667i	0.0214375	−	0.999770i	$-0.493176\pi$
$163$	−8.55843	−	3.54502i	−0.670348	−	0.277667i	−0.691786	+	0.722103i	$0.743176\pi$
$164$		0			0
$165$	−0.588812	+	0.243894i	−0.0458390	+	0.0189871i
$166$		0			0
$167$	0.530194	+	1.28000i	0.0410277	+	0.0990496i	0.943065	−	0.332608i	$-0.107929\pi$
$167$	0.530194	+	1.28000i	0.0410277	+	0.0990496i	−0.902037	+	0.431658i	$0.857929\pi$
$168$		0			0
$169$	−21.8148			−1.67806
$170$		0			0
$171$	−37.5831			−2.87405
$172$		0			0
$173$	−2.32011	−	5.60125i	−0.176395	−	0.425855i	0.810810	−	0.585309i	$-0.199027\pi$
$173$	−2.32011	−	5.60125i	−0.176395	−	0.425855i	−0.987205	+	0.159454i	$0.949027\pi$
$174$		0			0
$175$	8.73782	−	3.61932i	0.660517	−	0.273595i
$176$		0			0
$177$	−8.29786	−	3.43709i	−0.623705	−	0.258347i
$178$		0			0
$179$	14.6773	−	14.6773i	1.09703	−	1.09703i	0.102275	−	0.994756i	$-0.467388\pi$
$179$	14.6773	−	14.6773i	1.09703	−	1.09703i	0.994756	−	0.102275i	$-0.0326122\pi$
$180$		0			0
$181$	−0.163764	+	0.395362i	−0.0121725	+	0.0293870i	−0.929849	−	0.367942i	$-0.880063\pi$
$181$	−0.163764	+	0.395362i	−0.0121725	+	0.0293870i	0.917676	+	0.397329i	$0.130063\pi$
$182$		0			0
$183$			1.54733i			0.114382i
$184$		0			0
$185$	−0.474139	−	0.474139i	−0.0348594	−	0.0348594i
$186$		0			0
$187$	0.914630	−	3.73536i	0.0668844	−	0.273156i
$188$		0			0
$189$	−19.9534	−	19.9534i	−1.45140	−	1.45140i
$190$		0			0
$191$		−	6.28136i		−	0.454503i	−0.973836	−	0.227252i	$-0.927026\pi$
$191$		−	6.28136i		−	0.454503i	0.973836	−	0.227252i	$-0.0729740\pi$
$192$		0			0
$193$	2.95784	−	7.14086i	0.212910	−	0.514011i	−0.780958	−	0.624584i	$-0.785269\pi$
$193$	2.95784	−	7.14086i	0.212910	−	0.514011i	0.993868	+	0.110573i	$0.0352687\pi$
$194$		0			0
$195$	−2.85087	+	2.85087i	−0.204155	+	0.204155i
$196$		0			0
$197$	−14.1025	−	5.84146i	−1.00476	−	0.416186i	−0.181221	−	0.983442i	$-0.558005\pi$
$197$	−14.1025	−	5.84146i	−1.00476	−	0.416186i	−0.823542	+	0.567256i	$0.808005\pi$
$198$		0			0
$199$	11.4665	−	4.74956i	0.812836	−	0.336688i	0.0627511	−	0.998029i	$-0.480013\pi$
$199$	11.4665	−	4.74956i	0.812836	−	0.336688i	0.750085	+	0.661342i	$0.230013\pi$
$200$		0			0
$201$	5.39249	+	13.0186i	0.380357	+	0.918264i
$202$		0			0
$203$	−13.3527			−0.937175
$204$		0			0
$205$	1.60074			0.111801
$206$		0			0
$207$	12.9645	+	31.2990i	0.901094	+	2.17543i
$208$		0			0
$209$	4.28849	−	1.77635i	0.296641	−	0.122873i
$210$		0			0
$211$	12.2167	+	5.06030i	0.841029	+	0.348366i	0.761259	−	0.648448i	$-0.224581\pi$
$211$	12.2167	+	5.06030i	0.841029	+	0.348366i	0.0797698	+	0.996813i	$0.474581\pi$
$212$		0			0
$213$	−4.73394	+	4.73394i	−0.324364	+	0.324364i
$214$		0			0
$215$	−0.316882	+	0.765020i	−0.0216111	+	0.0521739i
$216$		0			0
$217$			6.54836i			0.444532i
$218$		0			0
$219$	−2.41562	−	2.41562i	−0.163232	−	0.163232i
$220$		0			0
$221$	−3.69724	−	24.0454i	−0.248704	−	1.61747i
$222$		0			0
$223$	−1.41967	−	1.41967i	−0.0950683	−	0.0950683i	0.657973	−	0.753041i	$-0.271414\pi$
$223$	−1.41967	−	1.41967i	−0.0950683	−	0.0950683i	−0.753041	+	0.657973i	$0.771414\pi$
$224$		0			0
$225$		−	37.4252i		−	2.49501i
$226$		0			0
$227$	5.61153	−	13.5474i	0.372450	−	0.899174i	−0.620884	−	0.783903i	$-0.713226\pi$
$227$	5.61153	−	13.5474i	0.372450	−	0.899174i	0.993334	−	0.115272i	$-0.0367739\pi$
$228$		0			0
$229$	19.6122	−	19.6122i	1.29601	−	1.29601i	0.365004	−	0.931006i	$-0.381068\pi$
$229$	19.6122	−	19.6122i	1.29601	−	1.29601i	0.931006	−	0.365004i	$-0.118932\pi$
$230$		0			0
$231$	5.34207	+	2.21276i	0.351482	+	0.145589i
$232$		0			0
$233$	−11.9663	+	4.95659i	−0.783936	+	0.324717i	−0.738503	−	0.674250i	$-0.764467\pi$
$233$	−11.9663	+	4.95659i	−0.783936	+	0.324717i	−0.0454332	+	0.998967i	$0.514467\pi$
$234$		0			0
$235$	0.768313	+	1.85487i	0.0501192	+	0.120998i
$236$		0			0
$237$	41.2144			2.67716
$238$		0			0
$239$	−11.1249			−0.719609			−0.359805	−	0.933028i	$-0.617157\pi$
$239$	−11.1249			−0.719609			−0.359805	+	0.933028i	$0.617157\pi$
$240$		0			0
$241$	2.40511	+	5.80646i	0.154927	+	0.374027i	0.982217	−	0.187748i	$-0.0601188\pi$
$241$	2.40511	+	5.80646i	0.154927	+	0.374027i	−0.827290	+	0.561775i	$0.810119\pi$
$242$		0			0
$243$	−35.1714	+	14.5685i	−2.25625	+	0.934567i
$244$		0			0
$245$	−0.652565	−	0.270301i	−0.0416909	−	0.0172689i
$246$		0			0
$247$	20.7637	−	20.7637i	1.32116	−	1.32116i
$248$		0			0
$249$	1.17222	−	2.82998i	0.0742861	−	0.179343i
$250$		0			0
$251$			21.1137i			1.33268i	0.745647	+	0.666341i	$0.232140\pi$
$251$			21.1137i			1.33268i	−0.745647	+	0.666341i	$0.767860\pi$
$252$		0			0
$253$	−2.95868	−	2.95868i	−0.186010	−	0.186010i
$254$		0			0
$255$	−2.27175	−	1.66624i	−0.142263	−	0.104344i
$256$		0			0
$257$	−2.69636	−	2.69636i	−0.168194	−	0.168194i	0.617991	−	0.786185i	$-0.287947\pi$
$257$	−2.69636	−	2.69636i	−0.168194	−	0.168194i	−0.786185	+	0.617991i	$0.787947\pi$
$258$		0			0
$259$			6.08350i			0.378010i
$260$		0			0
$261$	−20.2202	+	48.8158i	−1.25160	+	3.02162i
$262$		0			0
$263$	−13.8103	+	13.8103i	−0.851580	+	0.851580i	−0.990328	−	0.138748i	$-0.955692\pi$
$263$	−13.8103	+	13.8103i	−0.851580	+	0.851580i	0.138748	+	0.990328i	$0.455692\pi$
$264$		0			0
$265$	0.607762	+	0.251743i	0.0373345	+	0.0154645i
$266$		0			0
$267$	10.5380	−	4.36497i	0.644914	−	0.267132i
$268$		0			0
$269$	−1.16394	−	2.81000i	−0.0709666	−	0.171329i	0.884416	−	0.466699i	$-0.154557\pi$
$269$	−1.16394	−	2.81000i	−0.0709666	−	0.171329i	−0.955383	+	0.295371i	$0.904557\pi$
$270$		0			0
$271$	−25.6210			−1.55636			−0.778181	−	0.628040i	$-0.783857\pi$
$271$	−25.6210			−1.55636			−0.778181	+	0.628040i	$0.783857\pi$
$272$		0			0
$273$	36.5784			2.21382
$274$		0			0
$275$	1.76889	+	4.27047i	0.106668	+	0.257519i
$276$		0			0
$277$	−16.3687	+	6.78016i	−0.983503	+	0.407380i	−0.815722	−	0.578444i	$-0.803660\pi$
$277$	−16.3687	+	6.78016i	−0.983503	+	0.407380i	−0.167781	+	0.985824i	$0.553660\pi$
$278$		0			0
$279$	23.9400	+	9.91627i	1.43325	+	0.593672i
$280$		0			0
$281$	−16.8186	+	16.8186i	−1.00331	+	1.00331i	−0.00331728	+	0.999994i	$0.501056\pi$
$281$	−16.8186	+	16.8186i	−1.00331	+	1.00331i	−0.999994	+	0.00331728i	$0.998944\pi$
$282$		0			0
$283$	−2.61881	+	6.32238i	−0.155672	+	0.375826i	−0.982403	−	0.186771i	$-0.940198\pi$
$283$	−2.61881	+	6.32238i	−0.155672	+	0.375826i	0.826731	+	0.562597i	$0.190198\pi$
$284$		0			0
$285$		−	3.40054i		−	0.201431i
$286$		0			0
$287$	−10.2693	−	10.2693i	−0.606175	−	0.606175i
$288$		0			0
$289$	16.2147	−	5.10713i	0.953807	−	0.300419i
$290$		0			0
$291$	6.61878	+	6.61878i	0.388000	+	0.388000i
$292$		0			0
$293$			20.7411i			1.21171i	0.795576	+	0.605854i	$0.207169\pi$
$293$			20.7411i			1.21171i	−0.795576	+	0.605854i	$0.792831\pi$
$294$		0			0
$295$	0.222572	−	0.537337i	0.0129587	−	0.0312850i
$296$		0			0
$297$	9.75193	−	9.75193i	0.565864	−	0.565864i
$298$		0			0
$299$	−24.4545	−	10.1294i	−1.41424	−	0.585797i
$300$		0			0
$301$	6.94073	−	2.87495i	0.400057	−	0.165709i
$302$		0			0
$303$	2.21725	+	5.35292i	0.127378	+	0.307517i
$304$		0			0
$305$	−0.100199			−0.00573739
$306$		0			0
$307$	−7.66945			−0.437719			−0.218859	−	0.975756i	$-0.570234\pi$
$307$	−7.66945			−0.437719			−0.218859	+	0.975756i	$0.570234\pi$
$308$		0			0
$309$	−15.3229	−	36.9927i	−0.871687	−	2.10444i
$310$		0			0
$311$	25.9084	−	10.7316i	1.46913	−	0.608534i	0.502470	−	0.864595i	$-0.332425\pi$
$311$	25.9084	−	10.7316i	1.46913	−	0.608534i	0.966661	+	0.256061i	$0.0824247\pi$
$312$		0			0
$313$	23.4656	+	9.71978i	1.32636	+	0.549394i	0.929614	−	0.368536i	$-0.120141\pi$
$313$	23.4656	+	9.71978i	1.32636	+	0.549394i	0.396742	+	0.917930i	$0.370141\pi$
$314$		0			0
$315$	2.14369	−	2.14369i	0.120784	−	0.120784i
$316$		0			0
$317$	−4.68712	+	11.3157i	−0.263255	+	0.635554i	−0.999136	−	0.0415570i	$-0.986768\pi$
$317$	−4.68712	+	11.3157i	−0.263255	+	0.635554i	0.735881	+	0.677111i	$0.236768\pi$
$318$		0			0
$319$		−	6.52592i		−	0.365381i
$320$		0			0
$321$	−20.2103	−	20.2103i	−1.12803	−	1.12803i
$322$		0			0
$323$	16.5458	+	12.1357i	0.920636	+	0.675251i
$324$		0			0
$325$	20.6765	+	20.6765i	1.14692	+	1.14692i
$326$		0			0
$327$			59.9039i			3.31269i
$328$		0			0
$329$	6.97061	−	16.8285i	0.384302	−	0.927787i
$330$		0			0
$331$	−8.58090	+	8.58090i	−0.471649	+	0.471649i	−0.902448	−	0.430799i	$-0.858232\pi$
$331$	−8.58090	+	8.58090i	−0.471649	+	0.471649i	0.430799	+	0.902448i	$0.358232\pi$
$332$		0			0
$333$	22.2405	+	9.21233i	1.21877	+	0.504833i
$334$		0			0
$335$	−0.843036	+	0.349197i	−0.0460600	+	0.0190787i
$336$		0			0
$337$	−7.16538	−	17.2988i	−0.390323	−	0.942323i	−0.989869	−	0.141983i	$-0.954652\pi$
$337$	−7.16538	−	17.2988i	−0.390323	−	0.942323i	0.599546	−	0.800340i	$-0.295348\pi$
$338$		0			0
$339$	46.9698			2.55105
$340$		0			0
$341$	−3.20041			−0.173312
$342$		0			0
$343$	7.56463	+	18.2626i	0.408452	+	0.986090i
$344$		0			0
$345$	−2.83196	+	1.17303i	−0.152467	+	0.0631541i
$346$		0			0
$347$	−31.4538	−	13.0286i	−1.68853	−	0.699411i	−0.688852	−	0.724902i	$-0.741885\pi$
$347$	−31.4538	−	13.0286i	−1.68853	−	0.699411i	−0.999675	+	0.0254913i	$0.991885\pi$
$348$		0			0
$349$	−5.08598	+	5.08598i	−0.272246	+	0.272246i	−0.830004	−	0.557758i	$-0.811662\pi$
$349$	−5.08598	+	5.08598i	−0.272246	+	0.272246i	0.557758	+	0.830004i	$0.311662\pi$
$350$		0			0
$351$	33.3869	−	80.6031i	1.78206	−	4.30227i
$352$		0			0
$353$		−	2.93929i		−	0.156443i	−0.996936	−	0.0782213i	$-0.975076\pi$
$353$		−	2.93929i		−	0.156443i	0.996936	−	0.0782213i	$-0.0249241\pi$
$354$		0			0
$355$	−0.306552	−	0.306552i	−0.0162701	−	0.0162701i
$356$		0			0
$357$	3.88454	+	25.2635i	0.205591	+	1.33708i
$358$		0			0
$359$	15.9543	+	15.9543i	0.842034	+	0.842034i	0.989123	−	0.147090i	$-0.0469906\pi$
$359$	15.9543	+	15.9543i	0.842034	+	0.842034i	−0.147090	+	0.989123i	$0.546991\pi$
$360$		0			0
$361$			5.76714i			0.303534i
$362$		0			0
$363$	12.5926	−	30.4012i	0.660940	−	1.59565i
$364$		0			0
$365$	0.156426	−	0.156426i	0.00818771	−	0.00818771i
$366$		0			0
$367$	−7.27709	−	3.01427i	−0.379861	−	0.157343i	0.184579	−	0.982818i	$-0.440908\pi$
$367$	−7.27709	−	3.01427i	−0.379861	−	0.157343i	−0.564440	+	0.825474i	$0.690908\pi$
$368$		0			0
$369$	−53.0940	+	21.9923i	−2.76396	+	1.14487i
$370$		0			0
$371$	−2.28397	−	5.51400i	−0.118578	−	0.286272i
$372$		0			0
$373$	−7.47898			−0.387247			−0.193624	−	0.981076i	$-0.562024\pi$
$373$	−7.47898			−0.387247			−0.193624	+	0.981076i	$0.562024\pi$
$374$		0			0
$375$	6.80274			0.351292
$376$		0			0
$377$	−15.7984	−	38.1406i	−0.813657	−	1.96434i
$378$		0			0
$379$	−17.3882	+	7.20244i	−0.893173	+	0.369964i	−0.781591	−	0.623791i	$-0.785592\pi$
$379$	−17.3882	+	7.20244i	−0.893173	+	0.369964i	−0.111582	+	0.993755i	$0.535592\pi$
$380$		0			0
$381$	−47.5755	−	19.7064i	−2.43737	−	1.00959i
$382$		0			0
$383$	−18.0571	+	18.0571i	−0.922676	+	0.922676i	−0.997218	−	0.0745418i	$-0.976251\pi$
$383$	−18.0571	+	18.0571i	−0.922676	+	0.922676i	0.0745418	+	0.997218i	$0.476251\pi$
$384$		0			0
$385$	−0.143290	+	0.345931i	−0.00730271	+	0.0176303i
$386$		0			0
$387$		−	29.7280i		−	1.51116i
$388$		0			0
$389$	−8.25541	−	8.25541i	−0.418566	−	0.418566i	0.466143	−	0.884709i	$-0.345643\pi$
$389$	−8.25541	−	8.25541i	−0.418566	−	0.418566i	−0.884709	+	0.466143i	$0.845643\pi$
$390$		0			0
$391$	4.39901	−	17.9656i	0.222468	−	0.908560i
$392$		0			0
$393$	5.51873	+	5.51873i	0.278383	+	0.278383i
$394$		0			0
$395$			2.66888i			0.134286i
$396$		0			0
$397$	−9.37788	+	22.6402i	−0.470662	+	1.13628i	0.493209	+	0.869911i	$0.335824\pi$
$397$	−9.37788	+	22.6402i	−0.470662	+	1.13628i	−0.963871	+	0.266368i	$0.914176\pi$
$398$		0			0
$399$	−21.8155	+	21.8155i	−1.09214	+	1.09214i
$400$		0			0
$401$	33.9689	+	14.0704i	1.69632	+	0.702640i	0.999888	−	0.0149789i	$-0.00476810\pi$
$401$	33.9689	+	14.0704i	1.69632	+	0.702640i	0.696436	+	0.717619i	$0.254768\pi$
$402$		0			0
$403$	−18.7047	+	7.74775i	−0.931749	+	0.385943i
$404$		0			0
$405$	−2.04265	−	4.93138i	−0.101500	−	0.245042i
$406$		0			0
$407$	−2.97322			−0.147377
$408$		0			0
$409$	29.9345			1.48016			0.740082	−	0.672517i	$-0.234787\pi$
$409$	29.9345			1.48016			0.740082	+	0.672517i	$0.234787\pi$
$410$		0			0
$411$	−15.8270	−	38.2098i	−0.780689	−	1.88475i
$412$		0			0
$413$	−4.87506	+	2.01931i	−0.239886	+	0.0993639i
$414$		0			0
$415$	0.183258	+	0.0759081i	0.00899580	+	0.00372618i
$416$		0			0
$417$	7.55108	−	7.55108i	0.369778	−	0.369778i
$418$		0			0
$419$	−7.89257	+	19.0544i	−0.385578	+	0.930866i	0.605287	+	0.796007i	$0.293058\pi$
$419$	−7.89257	+	19.0544i	−0.385578	+	0.930866i	−0.990865	+	0.134859i	$0.956942\pi$
$420$		0			0
$421$			26.1468i			1.27432i	0.770732	+	0.637160i	$0.219891\pi$
$421$			26.1468i			1.27432i	−0.770732	+	0.637160i	$0.780109\pi$
$422$		0			0
$423$	−50.9674	−	50.9674i	−2.47812	−	2.47812i
$424$		0			0
$425$	−12.0848	+	16.4763i	−0.586197	+	0.799220i
$426$		0			0
$427$	0.642809	+	0.642809i	0.0311077	+	0.0311077i
$428$		0			0
$429$			17.8771i			0.863116i
$430$		0			0
$431$	−12.0058	+	28.9846i	−0.578299	+	1.39614i	0.316039	+	0.948746i	$0.397647\pi$
$431$	−12.0058	+	28.9846i	−0.578299	+	1.39614i	−0.894338	+	0.447392i	$0.852353\pi$
$432$		0			0
$433$	−3.87042	+	3.87042i	−0.186001	+	0.186001i	−0.793965	−	0.607964i	$-0.791986\pi$
$433$	−3.87042	+	3.87042i	−0.186001	+	0.186001i	0.607964	+	0.793965i	$0.291986\pi$
$434$		0			0
$435$	−4.41688	−	1.82953i	−0.211773	−	0.0877194i
$436$		0			0
$437$	20.6260	−	8.54356i	0.986674	−	0.408694i
$438$		0			0
$439$	−10.7515	−	25.9564i	−0.513142	−	1.23883i	−0.942046	−	0.335484i	$-0.891100\pi$
$439$	−10.7515	−	25.9564i	−0.513142	−	1.23883i	0.428904	−	0.903350i	$-0.358900\pi$
$440$		0			0
$441$	25.3581			1.20753
$442$		0			0
$443$	26.1894			1.24429			0.622147	−	0.782901i	$-0.286261\pi$
$443$	26.1894			1.24429			0.622147	+	0.782901i	$0.286261\pi$
$444$		0			0
$445$	0.282659	+	0.682399i	0.0133993	+	0.0323488i
$446$		0			0
$447$	−6.76210	+	2.80095i	−0.319837	+	0.132481i
$448$		0			0
$449$	−9.73085	−	4.03065i	−0.459227	−	0.190218i	0.141063	−	0.990001i	$-0.454948\pi$
$449$	−9.73085	−	4.03065i	−0.459227	−	0.190218i	−0.600290	+	0.799783i	$0.704948\pi$
$450$		0			0
$451$	5.01894	−	5.01894i	0.236333	−	0.236333i
$452$		0			0
$453$	21.6925	−	52.3704i	1.01920	−	2.46058i
$454$		0			0
$455$			2.36867i			0.111045i
$456$		0			0
$457$	−7.76216	−	7.76216i	−0.363099	−	0.363099i	0.501854	−	0.864952i	$-0.332652\pi$
$457$	−7.76216	−	7.76216i	−0.363099	−	0.363099i	−0.864952	+	0.501854i	$0.832652\pi$
$458$		0			0
$459$	59.2155	+	14.4994i	2.76394	+	0.676772i
$460$		0			0
$461$	18.9525	+	18.9525i	0.882704	+	0.882704i	0.993809	−	0.111104i	$-0.0354388\pi$
$461$	18.9525	+	18.9525i	0.882704	+	0.882704i	−0.111104	+	0.993809i	$0.535439\pi$
$462$		0			0
$463$		−	29.0845i		−	1.35167i	−0.737053	−	0.675835i	$-0.763783\pi$
$463$		−	29.0845i		−	1.35167i	0.737053	−	0.675835i	$-0.236217\pi$
$464$		0			0
$465$	−0.897231	+	2.16611i	−0.0416081	+	0.100451i
$466$		0			0
$467$	24.9433	−	24.9433i	1.15424	−	1.15424i	0.168546	−	0.985694i	$-0.446093\pi$
$467$	24.9433	−	24.9433i	1.15424	−	1.15424i	0.985694	−	0.168546i	$-0.0539072\pi$
$468$		0			0
$469$	7.64854	+	3.16813i	0.353177	+	0.146291i
$470$		0			0
$471$	7.58982	−	3.14381i	0.349720	−	0.144859i
$472$		0			0
$473$	1.40509	+	3.39218i	0.0646059	+	0.155972i
$474$		0			0
$475$	−24.6631			−1.13162
$476$		0			0
$477$	−23.6171			−1.08135
$478$		0			0
$479$	3.23701	+	7.81483i	0.147903	+	0.357069i	0.980416	−	0.196936i	$-0.0630991\pi$
$479$	3.23701	+	7.81483i	0.147903	+	0.357069i	−0.832514	+	0.554004i	$0.813099\pi$
$480$		0			0
$481$	−17.3769	+	7.19775i	−0.792319	+	0.328189i
$482$		0			0
$483$	25.6933	+	10.6425i	1.16908	+	0.484250i
$484$		0			0
$485$	−0.428606	+	0.428606i	−0.0194620	+	0.0194620i
$486$		0			0
$487$	−0.271796	+	0.656174i	−0.0123163	+	0.0297341i	−0.929918	−	0.367767i	$-0.880122\pi$
$487$	−0.271796	+	0.656174i	−0.0123163	+	0.0297341i	0.917602	+	0.397501i	$0.130122\pi$
$488$		0			0
$489$			30.0915i			1.36078i
$490$		0			0
$491$	5.18209	+	5.18209i	0.233864	+	0.233864i	0.814304	−	0.580439i	$-0.197119\pi$
$491$	5.18209	+	5.18209i	0.233864	+	0.233864i	−0.580439	+	0.814304i	$0.697119\pi$
$492$		0			0
$493$	24.6647	−	14.9618i	1.11084	−	0.673847i
$494$		0			0
$495$	1.04770	+	1.04770i	0.0470905	+	0.0470905i
$496$		0			0
$497$			3.93325i			0.176430i
$498$		0			0
$499$	−4.16355	+	10.0517i	−0.186386	+	0.449976i	−0.989259	−	0.146175i	$-0.953304\pi$
$499$	−4.16355	+	10.0517i	−0.186386	+	0.449976i	0.802873	+	0.596150i	$0.203304\pi$
$500$		0			0
$501$	3.18233	−	3.18233i	0.142176	−	0.142176i
$502$		0			0
$503$	−32.6599	−	13.5282i	−1.45623	−	0.603192i	−0.492561	−	0.870278i	$-0.663939\pi$
$503$	−32.6599	−	13.5282i	−1.45623	−	0.603192i	−0.963673	+	0.267086i	$0.913939\pi$
$504$		0			0
$505$	−0.346634	+	0.143581i	−0.0154250	+	0.00638926i
$506$		0			0
$507$	27.1178	+	65.4682i	1.20434	+	2.90755i
$508$		0			0
$509$	7.29615			0.323396			0.161698	−	0.986840i	$-0.448303\pi$
$509$	7.29615			0.323396			0.161698	+	0.986840i	$0.448303\pi$
$510$		0			0
$511$	−2.00704			−0.0887863
$512$		0			0
$513$	28.1600	+	67.9841i	1.24329	+	3.00157i
$514$		0			0
$515$	2.39550	−	0.992249i	0.105558	−	0.0437237i
$516$		0			0
$517$	8.22469	+	3.40678i	0.361721	+	0.149830i
$518$		0			0
$519$	−13.9258	+	13.9258i	−0.611273	+	0.611273i
$520$		0			0
$521$	5.58727	−	13.4889i	0.244783	−	0.590957i	−0.752963	−	0.658062i	$-0.771376\pi$
$521$	5.58727	−	13.4889i	0.244783	−	0.590957i	0.997746	+	0.0671051i	$0.0213763\pi$
$522$		0			0
$523$			8.79889i			0.384749i	0.981322	+	0.192374i	$0.0616188\pi$
$523$			8.79889i			0.384749i	−0.981322	+	0.192374i	$0.938381\pi$
$524$		0			0
$525$	−21.7239	−	21.7239i	−0.948108	−	0.948108i
$526$		0			0
$527$	−7.33751	−	12.0959i	−0.319627	−	0.526908i
$528$		0			0
$529$	2.03338	+	2.03338i	0.0884078	+	0.0884078i
$530$		0			0
$531$			20.8805i			0.906136i
$532$		0			0
$533$	17.1829	−	41.4833i	0.744275	−	1.79684i
$534$		0			0
$535$	1.30874	−	1.30874i	0.0565817	−	0.0565817i
$536$		0			0
$537$	−62.2932	−	25.8027i	−2.68815	−	1.11347i
$538$		0			0
$539$	−2.89354	+	1.19854i	−0.124634	+	0.0516249i
$540$		0			0
$541$	−7.84504	−	18.9396i	−0.337285	−	0.814277i	−0.997974	−	0.0636182i	$-0.979736\pi$
$541$	−7.84504	−	18.9396i	−0.337285	−	0.814277i	0.660690	−	0.750659i	$-0.270264\pi$
$542$		0			0
$543$	1.39009			0.0596547
$544$		0			0
$545$	−3.87914			−0.166164
$546$		0			0
$547$	2.50793	+	6.05467i	0.107231	+	0.258879i	0.968383	−	0.249469i	$-0.0802562\pi$
$547$	2.50793	+	6.05467i	0.107231	+	0.258879i	−0.861151	+	0.508348i	$0.830256\pi$
$548$		0			0
$549$	3.32345	−	1.37662i	0.141841	−	0.0587526i
$550$		0			0
$551$	32.1695	+	13.3250i	1.37046	+	0.567665i
$552$		0			0
$553$	17.1217	−	17.1217i	0.728090	−	0.728090i
$554$		0			0
$555$	−0.833538	+	2.01234i	−0.0353817	+	0.0854190i
$556$		0			0
$557$			30.7206i			1.30167i	0.759217	+	0.650837i	$0.225582\pi$
$557$			30.7206i			1.30167i	−0.759217	+	0.650837i	$0.774418\pi$
$558$		0			0
$559$	16.4240	+	16.4240i	0.694661	+	0.694661i
$560$		0			0
$561$	−12.3471	+	1.89851i	−0.521297	+	0.0801551i
$562$		0			0
$563$	−7.18380	−	7.18380i	−0.302761	−	0.302761i	0.539332	−	0.842093i	$-0.318677\pi$
$563$	−7.18380	−	7.18380i	−0.302761	−	0.302761i	−0.842093	+	0.539332i	$0.818677\pi$
$564$		0			0
$565$			3.04158i			0.127960i
$566$		0			0
$567$	−18.5321	+	44.7406i	−0.778277	+	1.87893i
$568$		0			0
$569$	−0.480241	+	0.480241i	−0.0201328	+	0.0201328i	−0.717102	−	0.696969i	$-0.754532\pi$
$569$	−0.480241	+	0.480241i	−0.0201328	+	0.0201328i	0.696969	+	0.717102i	$0.254532\pi$
$570$		0			0
$571$	1.80310	+	0.746868i	0.0754574	+	0.0312555i	0.420093	−	0.907481i	$-0.361997\pi$
$571$	1.80310	+	0.746868i	0.0754574	+	0.0312555i	−0.344636	+	0.938737i	$0.611997\pi$
$572$		0			0
$573$	−18.8510	+	7.80833i	−0.787511	+	0.326198i
$574$		0			0
$575$	8.50766	+	20.5393i	0.354794	+	0.856549i
$576$		0			0
$577$	−23.1548			−0.963949			−0.481974	−	0.876185i	$-0.660080\pi$
$577$	−23.1548			−0.963949			−0.481974	+	0.876185i	$0.660080\pi$
$578$		0			0
$579$	−25.1073			−1.04342
$580$		0			0
$581$	−0.688685	−	1.66263i	−0.0285715	−	0.0689777i
$582$		0			0
$583$	2.69488	−	1.11626i	0.111611	−	0.0462306i
$584$		0			0
$585$	8.65958	+	3.58692i	0.358030	+	0.148301i
$586$		0			0
$587$	21.2905	−	21.2905i	0.878755	−	0.878755i	−0.114651	−	0.993406i	$-0.536575\pi$
$587$	21.2905	−	21.2905i	0.878755	−	0.878755i	0.993406	+	0.114651i	$0.0365749\pi$
$588$		0			0
$589$	6.53479	−	15.7764i	0.269261	−	0.650055i
$590$		0			0
$591$			49.5845i			2.03963i
$592$		0			0
$593$	−15.4081	−	15.4081i	−0.632735	−	0.632735i	0.316018	−	0.948753i	$-0.397654\pi$
$593$	−15.4081	−	15.4081i	−0.632735	−	0.632735i	−0.948753	+	0.316018i	$0.897654\pi$
$594$		0			0
$595$	−1.63596	+	0.251547i	−0.0670680	+	0.0103124i
$596$		0			0
$597$	−28.5078	−	28.5078i	−1.16675	−	1.16675i
$598$		0			0
$599$		−	18.0195i		−	0.736256i	−0.929775	−	0.368128i	$-0.879999\pi$
$599$		−	18.0195i		−	0.736256i	0.929775	−	0.368128i	$-0.120001\pi$
$600$		0			0
$601$	−11.7759	+	28.4296i	−0.480351	+	1.15967i	0.479092	+	0.877765i	$0.340966\pi$
$601$	−11.7759	+	28.4296i	−0.480351	+	1.15967i	−0.959443	+	0.281904i	$0.909034\pi$
$602$		0			0
$603$	23.1646	−	23.1646i	0.943335	−	0.943335i
$604$		0			0
$605$	1.96866	+	0.815447i	0.0800376	+	0.0331527i
$606$		0			0
$607$	−0.794404	+	0.329053i	−0.0322439	+	0.0133558i	−0.398747	−	0.917061i	$-0.630555\pi$
$607$	−0.794404	+	0.329053i	−0.0322439	+	0.0133558i	0.366503	+	0.930417i	$0.380555\pi$
$608$		0			0
$609$	16.5987	+	40.0727i	0.672611	+	1.62383i
$610$		0			0
$611$	56.3164			2.27832
$612$		0			0
$613$	22.9664			0.927604			0.463802	−	0.885939i	$-0.346485\pi$
$613$	22.9664			0.927604			0.463802	+	0.885939i	$0.346485\pi$
$614$		0			0
$615$	−1.98987	−	4.80398i	−0.0802395	−	0.193715i
$616$		0			0
$617$	7.62860	−	3.15987i	0.307116	−	0.127212i	−0.223802	−	0.974635i	$-0.571847\pi$
$617$	7.62860	−	3.15987i	0.307116	−	0.127212i	0.530918	+	0.847423i	$0.321847\pi$
$618$		0			0
$619$	−35.9242	−	14.8803i	−1.44392	−	0.598090i	−0.483172	−	0.875525i	$-0.660516\pi$
$619$	−35.9242	−	14.8803i	−1.44392	−	0.598090i	−0.960744	+	0.277435i	$0.910516\pi$
$620$		0			0
$621$	46.9030	−	46.9030i	1.88215	−	1.88215i
$622$		0			0
$623$	2.56445	−	6.19114i	0.102743	−	0.248043i
$624$		0			0
$625$		−	24.3382i		−	0.973530i
$626$		0			0
$627$	−10.6620	−	10.6620i	−0.425799	−	0.425799i
$628$		0			0
$629$	−6.81663	−	11.2373i	−0.271797	−	0.448059i
$630$		0			0
$631$	−17.7503	−	17.7503i	−0.706628	−	0.706628i	0.259196	−	0.965825i	$-0.416542\pi$
$631$	−17.7503	−	17.7503i	−0.706628	−	0.706628i	−0.965825	+	0.259196i	$0.916542\pi$
$632$		0			0
$633$		−	42.9538i		−	1.70726i
$634$		0			0
$635$	1.27611	−	3.08081i	0.0506409	−	0.122258i
$636$		0			0
$637$	−14.0097	+	14.0097i	−0.555086	+	0.555086i
$638$		0			0
$639$	14.3795	+	5.95617i	0.568843	+	0.235623i
$640$		0			0
$641$	39.3125	−	16.2838i	1.55275	−	0.643171i	0.568940	−	0.822379i	$-0.307354\pi$
$641$	39.3125	−	16.2838i	1.55275	−	0.643171i	0.983811	+	0.179208i	$0.0573536\pi$
$642$		0			0
$643$	−14.9350	−	36.0563i	−0.588979	−	1.42192i	−0.884480	−	0.466579i	$-0.845486\pi$
$643$	−14.9350	−	36.0563i	−0.588979	−	1.42192i	0.295501	−	0.955342i	$-0.404514\pi$
$644$		0			0
$645$	2.68981			0.105911
$646$		0			0
$647$	17.8336			0.701110			0.350555	−	0.936542i	$-0.385993\pi$
$647$	17.8336			0.701110			0.350555	+	0.936542i	$0.385993\pi$
$648$		0			0
$649$	−0.986909	−	2.38261i	−0.0387396	−	0.0935256i
$650$		0			0
$651$	19.6523	−	8.14023i	0.770233	−	0.319041i
$652$		0			0
$653$	20.3002	+	8.40863i	0.794409	+	0.329055i	0.742715	−	0.669608i	$-0.233538\pi$
$653$	20.3002	+	8.40863i	0.794409	+	0.329055i	0.0516945	+	0.998663i	$0.483538\pi$
$654$		0			0
$655$	−0.357372	+	0.357372i	−0.0139637	+	0.0139637i
$656$		0			0
$657$	−3.03929	+	7.33750i	−0.118574	+	0.286263i
$658$		0			0
$659$			15.7563i			0.613778i	0.951745	+	0.306889i	$0.0992880\pi$
$659$			15.7563i			0.613778i	−0.951745	+	0.306889i	$0.900712\pi$
$660$		0			0
$661$	25.1529	+	25.1529i	0.978336	+	0.978336i	0.999770	−	0.0214341i	$-0.00682320\pi$
$661$	25.1529	+	25.1529i	0.978336	+	0.978336i	−0.0214341	+	0.999770i	$0.506823\pi$
$662$		0			0
$663$	−67.5666	+	40.9865i	−2.62407	+	1.59178i
$664$		0			0
$665$	−1.41269	−	1.41269i	−0.0547817	−	0.0547817i
$666$		0			0
$667$		−	31.3871i		−	1.21531i
$668$		0			0
$669$	−2.49579	+	6.02537i	−0.0964927	+	0.232954i
$670$		0			0
$671$	−0.314163	+	0.314163i	−0.0121281	+	0.0121281i
$672$		0			0
$673$	−16.4981	−	6.83374i	−0.635955	−	0.263421i	0.0413258	−	0.999146i	$-0.486842\pi$
$673$	−16.4981	−	6.83374i	−0.635955	−	0.263421i	−0.677281	+	0.735724i	$0.736842\pi$
$674$		0			0
$675$	−67.6985	+	28.0417i	−2.60572	+	1.07932i
$676$		0			0
$677$	−4.03458	−	9.74034i	−0.155061	−	0.374352i	0.827189	−	0.561923i	$-0.189938\pi$
$677$	−4.03458	−	9.74034i	−0.155061	−	0.374352i	−0.982251	+	0.187572i	$0.939938\pi$
$678$		0			0
$679$	5.49928			0.211043
$680$		0			0
$681$	−47.6328			−1.82529
$682$		0			0
$683$	5.47678	+	13.2221i	0.209563	+	0.505931i	0.993355	−	0.115094i	$-0.0367168\pi$
$683$	5.47678	+	13.2221i	0.209563	+	0.505931i	−0.783791	+	0.621024i	$0.786717\pi$
$684$		0			0
$685$	2.47432	−	1.02490i	0.0945387	−	0.0391592i
$686$		0			0
$687$	−83.2379	−	34.4783i	−3.17572	−	1.31543i
$688$		0			0
$689$	13.0479	−	13.0479i	0.497084	−	0.497084i
$690$		0			0
$691$	−10.4129	+	25.1389i	−0.396125	+	0.956330i	0.592451	+	0.805606i	$0.298160\pi$
$691$	−10.4129	+	25.1389i	−0.396125	+	0.956330i	−0.988576	+	0.150723i	$0.951840\pi$
$692$		0			0
$693$		−	13.4426i		−	0.510643i
$694$		0			0
$695$	0.488978	+	0.488978i	0.0185480	+	0.0185480i
$696$		0			0
$697$	30.4759	+	7.46226i	1.15436	+	0.282653i
$698$		0			0
$699$	29.7504	+	29.7504i	1.12526	+	1.12526i
$700$		0			0
$701$			15.3048i			0.578053i	0.957321	+	0.289027i	$0.0933316\pi$
$701$			15.3048i			0.578053i	−0.957321	+	0.289027i	$0.906668\pi$
$702$		0			0
$703$	6.07090	−	14.6564i	0.228968	−	0.552778i
$704$		0			0
$705$	4.61156	−	4.61156i	0.173681	−	0.173681i
$706$		0			0
$707$	3.14488	+	1.30265i	0.118275	+	0.0489913i
$708$		0			0
$709$	−40.5876	+	16.8119i	−1.52430	+	0.631385i	−0.978447	−	0.206498i	$-0.933793\pi$
$709$	−40.5876	+	16.8119i	−1.52430	+	0.631385i	−0.545851	+	0.837882i	$0.683793\pi$
$710$		0			0
$711$	−36.6673	−	88.5226i	−1.37513	−	3.31986i
$712$		0			0
$713$	−15.3927			−0.576462
$714$		0			0
$715$	−1.15765			−0.0432938
$716$		0			0
$717$	13.8293	+	33.3869i	0.516465	+	1.24686i
$718$		0			0
$719$	40.2586	−	16.6757i	1.50139	−	0.621897i	0.527632	−	0.849473i	$-0.323080\pi$
$719$	40.2586	−	16.6757i	1.50139	−	0.621897i	0.973760	+	0.227577i	$0.0730802\pi$
$720$		0			0
$721$	−21.7335	−	9.00230i	−0.809397	−	0.335263i
$722$		0			0
$723$	14.4360	−	14.4360i	0.536879	−	0.536879i
$724$		0			0
$725$	−13.2690	+	32.0343i	−0.492800	+	1.18972i
$726$		0			0
$727$		−	36.4200i		−	1.35074i	−0.737478	−	0.675371i	$-0.763984\pi$
$727$		−	36.4200i		−	1.35074i	0.737478	−	0.675371i	$-0.236016\pi$
$728$		0			0
$729$	33.6140	+	33.6140i	1.24496	+	1.24496i
$730$		0			0
$731$	−9.59932	+	13.0877i	−0.355044	+	0.484066i
$732$		0			0
$733$	−1.38111	−	1.38111i	−0.0510124	−	0.0510124i	0.681140	−	0.732153i	$-0.261484\pi$
$733$	−1.38111	−	1.38111i	−0.0510124	−	0.0510124i	−0.732153	+	0.681140i	$0.761484\pi$
$734$		0			0
$735$			2.29442i			0.0846310i
$736$		0			0
$737$	−1.54838	+	3.73811i	−0.0570351	+	0.137695i
$738$		0			0
$739$	14.8584	−	14.8584i	0.546573	−	0.546573i	−0.378875	−	0.925448i	$-0.623689\pi$
$739$	14.8584	−	14.8584i	0.546573	−	0.546573i	0.925448	+	0.378875i	$0.123689\pi$
$740$		0			0
$741$	−88.1251	−	36.5026i	−3.23736	−	1.34096i
$742$		0			0
$743$	−17.1974	+	7.12339i	−0.630911	+	0.261332i	−0.675140	−	0.737689i	$-0.735917\pi$
$743$	−17.1974	+	7.12339i	−0.630911	+	0.261332i	0.0442290	+	0.999021i	$0.485917\pi$
$744$		0			0
$745$	−0.181379	−	0.437887i	−0.00664521	−	0.0160430i
$746$		0			0
$747$	−7.12127			−0.260554
$748$		0			0
$749$	−16.7919			−0.613564
$750$		0			0
$751$	3.85528	+	9.30747i	0.140681	+	0.339635i	0.978479	−	0.206346i	$-0.0661572\pi$
$751$	3.85528	+	9.30747i	0.140681	+	0.339635i	−0.837798	+	0.545981i	$0.816157\pi$
$752$		0			0
$753$	63.3641	−	26.2463i	2.30912	−	0.956468i
$754$		0			0
$755$	3.39131	+	1.40472i	0.123422	+	0.0511232i
$756$		0			0
$757$	−26.5366	+	26.5366i	−0.964489	+	0.964489i	−0.999391	−	0.0349015i	$-0.988888\pi$
$757$	−26.5366	+	26.5366i	−0.964489	+	0.964489i	0.0349015	+	0.999391i	$0.488888\pi$
$758$		0			0
$759$	−5.20136	+	12.5572i	−0.188797	+	0.455797i
$760$		0			0
$761$		−	34.5368i		−	1.25196i	−0.779840	−	0.625979i	$-0.784700\pi$
$761$		−	34.5368i		−	1.25196i	0.779840	−	0.625979i	$-0.215300\pi$
$762$		0			0
$763$	24.8859	+	24.8859i	0.900930	+	0.900930i
$764$		0			0
$765$	−1.55774	+	6.36181i	−0.0563201	+	0.230012i
$766$		0			0
$767$	−11.5359	−	11.5359i	−0.416539	−	0.416539i
$768$		0			0
$769$			27.2618i			0.983084i	0.870854	+	0.491542i	$0.163567\pi$
$769$			27.2618i			0.983084i	−0.870854	+	0.491542i	$0.836433\pi$
$770$		0			0
$771$	−4.74020	+	11.4439i	−0.170714	+	0.412140i
$772$		0			0
$773$	−17.0532	+	17.0532i	−0.613361	+	0.613361i	−0.943820	−	0.330459i	$-0.892796\pi$
$773$	−17.0532	+	17.0532i	−0.613361	+	0.613361i	0.330459	+	0.943820i	$0.392796\pi$
$774$		0			0
$775$	15.7101	+	6.50734i	0.564324	+	0.233751i
$776$		0			0
$777$	18.2572	−	7.56237i	0.654972	−	0.271298i
$778$		0			0
$779$	14.4928	+	34.9888i	0.519260	+	1.25360i
$780$		0			0
$781$	−1.92231			−0.0687858
$782$		0			0
$783$	103.453			3.69712
$784$		0			0
$785$	0.203581	+	0.491487i	0.00726610	+	0.0175419i
$786$		0			0
$787$	30.7053	−	12.7185i	1.09452	−	0.453367i	0.238942	−	0.971034i	$-0.423199\pi$
$787$	30.7053	−	12.7185i	1.09452	−	0.453367i	0.855582	+	0.517667i	$0.173199\pi$
$788$		0			0
$789$	58.6136	+	24.2785i	2.08670	+	0.864339i
$790$		0			0
$791$	19.5127	−	19.5127i	0.693791	−	0.693791i
$792$		0			0
$793$	−1.07557	+	2.59667i	−0.0381948	+	0.0922103i
$794$		0			0
$795$		−	2.13689i		−	0.0757878i
$796$		0			0
$797$	13.8217	+	13.8217i	0.489589	+	0.489589i	0.908176	−	0.418588i	$-0.137475\pi$
$797$	13.8217	+	13.8217i	0.489589	+	0.489589i	−0.418588	+	0.908176i	$0.637475\pi$
$798$		0			0
$799$	5.98066	+	38.8958i	0.211581	+	1.37604i
$800$		0			0
$801$	−18.7507	−	18.7507i	−0.662522	−	0.662522i
$802$		0			0
$803$		−	0.980911i		−	0.0346156i
$804$		0			0
$805$	−0.689167	+	1.66380i	−0.0242899	+	0.0586411i
$806$		0			0
$807$	−6.98619	+	6.98619i	−0.245925	+	0.245925i
$808$		0			0
$809$	−5.90083	−	2.44420i	−0.207462	−	0.0859336i	0.276533	−	0.961005i	$-0.410815\pi$
$809$	−5.90083	−	2.44420i	−0.207462	−	0.0859336i	−0.483995	+	0.875071i	$0.660815\pi$
$810$		0			0
$811$	−21.4901	+	8.90148i	−0.754619	+	0.312573i	−0.726624	−	0.687035i	$-0.758912\pi$
$811$	−21.4901	+	8.90148i	−0.754619	+	0.312573i	−0.0279941	+	0.999608i	$0.508912\pi$
$812$		0			0
$813$	31.8493	+	76.8910i	1.11700	+	2.69668i
$814$		0			0
$815$	−1.94861			−0.0682567
$816$		0			0
$817$	−19.5907			−0.685392
$818$		0			0
$819$	−32.5427	−	78.5651i	−1.13713	−	2.74529i
$820$		0			0
$821$	−6.03718	+	2.50068i	−0.210699	+	0.0872744i	−0.485537	−	0.874216i	$-0.661376\pi$
$821$	−6.03718	+	2.50068i	−0.210699	+	0.0872744i	0.274838	+	0.961491i	$0.411376\pi$
$822$		0			0
$823$	0.422123	+	0.174849i	0.0147143	+	0.00609485i	0.390028	−	0.920803i	$-0.372465\pi$
$823$	0.422123	+	0.174849i	0.0147143	+	0.00609485i	−0.375314	+	0.926898i	$0.622465\pi$
$824$		0			0
$825$	10.6172	−	10.6172i	0.369644	−	0.369644i
$826$		0			0
$827$	12.6231	−	30.4748i	0.438947	−	1.05971i	−0.537365	−	0.843349i	$-0.680580\pi$
$827$	12.6231	−	30.4748i	0.438947	−	1.05971i	0.976313	−	0.216363i	$-0.0694196\pi$
$828$		0			0
$829$		−	47.3572i		−	1.64478i	−0.568922	−	0.822391i	$-0.692640\pi$
$829$		−	47.3572i		−	1.64478i	0.568922	−	0.822391i	$-0.307360\pi$
$830$		0			0
$831$	40.6958	+	40.6958i	1.41172	+	1.41172i
$832$		0			0
$833$	−11.1639	−	8.18826i	−0.386805	−	0.283706i
$834$		0			0
$835$	0.206075	+	0.206075i	0.00713153	+	0.00713153i
$836$		0			0
$837$		−	50.7351i		−	1.75366i
$838$		0			0
$839$	−9.00397	+	21.7375i	−0.310852	+	0.750462i	0.688822	+	0.724930i	$0.258128\pi$
$839$	−9.00397	+	21.7375i	−0.310852	+	0.750462i	−0.999674	+	0.0255320i	$0.991872\pi$
$840$		0			0
$841$	14.1090	−	14.1090i	0.486518	−	0.486518i
$842$		0			0
$843$	71.3812	+	29.5671i	2.45850	+	1.01834i
$844$		0			0
$845$	−4.23947	+	1.75604i	−0.145842	+	0.0604098i
$846$		0			0
$847$	−7.39824	−	17.8609i	−0.254207	−	0.613709i
$848$		0			0
$849$	22.2295			0.762914
$850$		0			0
$851$	−14.3000			−0.490198
$852$		0			0
$853$	18.1944	+	43.9253i	0.622966	+	1.50397i	0.848204	+	0.529669i	$0.177684\pi$
$853$	18.1944	+	43.9253i	0.622966	+	1.50397i	−0.225238	+	0.974304i	$0.572316\pi$
$854$		0			0
$855$	−7.30387	+	3.02536i	−0.249787	+	0.103465i
$856$		0			0
$857$	8.72159	+	3.61260i	0.297924	+	0.123404i	0.526638	−	0.850089i	$-0.323452\pi$
$857$	8.72159	+	3.61260i	0.297924	+	0.123404i	−0.228714	+	0.973494i	$0.573452\pi$
$858$		0			0
$859$	−5.99963	+	5.99963i	−0.204705	+	0.204705i	−0.802012	−	0.597307i	$-0.796237\pi$
$859$	−5.99963	+	5.99963i	−0.204705	+	0.204705i	0.597307	+	0.802012i	$0.296237\pi$
$860$		0			0
$861$	−18.0534	+	43.5847i	−0.615257	+	1.48536i
$862$		0			0
$863$			26.1327i			0.889569i	0.895638	+	0.444784i	$0.146720\pi$
$863$			26.1327i			0.889569i	−0.895638	+	0.444784i	$0.853280\pi$
$864$		0			0
$865$	−0.901779	−	0.901779i	−0.0306614	−	0.0306614i
$866$		0			0
$867$	−35.4834	−	42.3133i	−1.20508	−	1.43704i
$868$		0			0
$869$	8.36798	+	8.36798i	0.283864	+	0.283864i
$870$		0			0
$871$			25.5957i			0.867277i
$872$		0			0
$873$	8.32764	−	20.1047i	0.281848	−	0.680441i
$874$		0			0
$875$	2.82607	−	2.82607i	0.0955385	−	0.0955385i
$876$		0			0
$877$	−1.08601	−	0.449841i	−0.0366720	−	0.0151900i	0.364272	−	0.931293i	$-0.381318\pi$
$877$	−1.08601	−	0.449841i	−0.0366720	−	0.0151900i	−0.400944	+	0.916103i	$0.631318\pi$
$878$		0			0
$879$	62.2461	−	25.7832i	2.09951	−	0.869645i
$880$		0			0
$881$	6.51615	+	15.7314i	0.219535	+	0.530004i	0.994825	−	0.101601i	$-0.0323965\pi$
$881$	6.51615	+	15.7314i	0.219535	+	0.530004i	−0.775290	+	0.631605i	$0.782397\pi$
$882$		0			0
$883$	−47.7123			−1.60565			−0.802824	−	0.596216i	$-0.796670\pi$
$883$	−47.7123			−1.60565			−0.802824	+	0.596216i	$0.796670\pi$
$884$		0			0
$885$	−1.88928			−0.0635074
$886$		0			0
$887$	−4.35452	−	10.5127i	−0.146210	−	0.352983i	0.833760	−	0.552127i	$-0.186184\pi$
$887$	−4.35452	−	10.5127i	−0.146210	−	0.352983i	−0.979970	+	0.199144i	$0.936184\pi$
$888$		0			0
$889$	−27.9510	+	11.5777i	−0.937446	+	0.388303i
$890$		0			0
$891$	−21.8663	−	9.05730i	−0.732547	−	0.303431i
$892$		0			0
$893$	−33.5874	+	33.5874i	−1.12396	+	1.12396i
$894$		0			0
$895$	1.67088	−	4.03386i	0.0558514	−	0.134837i
$896$		0			0
$897$			85.9820i			2.87086i
$898$		0			0
$899$	−16.9758	−	16.9758i	−0.566174	−	0.566174i
$900$		0			0
$901$	10.3974	+	7.62608i	0.346387	+	0.254062i
$902$		0			0
$903$	−17.2560	−	17.2560i	−0.574243	−	0.574243i
$904$		0			0
$905$			0.0900171i			0.00299227i
$906$		0			0
$907$	−19.3009	+	46.5966i	−0.640877	+	1.54721i	0.184621	+	0.982810i	$0.440894\pi$
$907$	−19.3009	+	46.5966i	−0.640877	+	1.54721i	−0.825498	+	0.564404i	$0.809106\pi$
$908$		0			0
$909$	9.52468	−	9.52468i	0.315914	−	0.315914i
$910$		0			0
$911$	−16.7233	−	6.92701i	−0.554067	−	0.229502i	0.0880400	−	0.996117i	$-0.471940\pi$
$911$	−16.7233	−	6.92701i	−0.554067	−	0.229502i	−0.642107	+	0.766615i	$0.721940\pi$
$912$		0			0
$913$	0.812587	−	0.336584i	0.0268927	−	0.0111393i
$914$		0			0
$915$	0.124557	+	0.300708i	0.00411773	+	0.00994109i
$916$		0			0
$917$	4.58530			0.151420
$918$		0			0
$919$	21.6058			0.712710			0.356355	−	0.934351i	$-0.384019\pi$
$919$	21.6058			0.712710			0.356355	+	0.934351i	$0.384019\pi$
$920$		0			0
$921$	9.53386	+	23.0168i	0.314151	+	0.758428i
$922$		0			0
$923$	−11.2349	+	4.65366i	−0.369802	+	0.153177i
$924$		0			0
$925$	14.5949	+	6.04539i	0.479876	+	0.198771i
$926$		0			0
$927$	−65.8226	+	65.8226i	−2.16190	+	2.16190i
$928$		0			0
$929$	1.23930	−	2.99194i	0.0406602	−	0.0981624i	−0.902245	−	0.431224i	$-0.858082\pi$
$929$	1.23930	−	2.99194i	0.0406602	−	0.0981624i	0.942905	+	0.333062i	$0.108082\pi$
$930$		0			0
$931$		−	16.7109i		−	0.547679i
$932$		0			0
$933$	−64.4132	−	64.4132i	−2.10879	−	2.10879i
$934$		0			0
$935$	−0.122940	−	0.799552i	−0.00402057	−	0.0261482i
$936$		0			0
$937$	−8.20364	−	8.20364i	−0.268001	−	0.268001i	0.560293	−	0.828294i	$-0.310688\pi$
$937$	−8.20364	−	8.20364i	−0.268001	−	0.268001i	−0.828294	+	0.560293i	$0.810688\pi$
$938$		0			0
$939$		−	82.5052i		−	2.69246i
$940$		0			0
$941$	14.8003	−	35.7310i	0.482474	−	1.16480i	−0.475956	−	0.879469i	$-0.657898\pi$
$941$	14.8003	−	35.7310i	0.482474	−	1.16480i	0.958430	−	0.285327i	$-0.0921022\pi$
$942$		0			0
$943$	24.1391	−	24.1391i	0.786079	−	0.786079i
$944$		0			0
$945$	−5.48395	−	2.27153i	−0.178393	−	0.0738927i
$946$		0			0
$947$	−23.4101	+	9.69676i	−0.760724	+	0.315102i	−0.729109	−	0.684398i	$-0.760065\pi$
$947$	−23.4101	+	9.69676i	−0.760724	+	0.315102i	−0.0316156	+	0.999500i	$0.510065\pi$
$948$		0			0
$949$	−2.37465	−	5.73292i	−0.0770844	−	0.186098i
$950$		0			0
$951$	39.7861			1.29015
$952$		0			0
$953$	−41.0918			−1.33110			−0.665548	−	0.746355i	$-0.731802\pi$
$953$	−41.0918			−1.33110			−0.665548	+	0.746355i	$0.731802\pi$
$954$		0			0
$955$	−0.505637	−	1.22072i	−0.0163620	−	0.0395014i
$956$		0			0
$957$	−19.5849	+	8.11234i	−0.633090	+	0.262235i
$958$		0			0
$959$	−22.4485	−	9.29848i	−0.724901	−	0.300264i
$960$		0			0
$961$	13.5951	−	13.5951i	0.438553	−	0.438553i
$962$		0			0
$963$	−25.4283	+	61.3892i	−0.819414	+	1.97824i
$964$		0			0
$965$		−	1.62585i		−	0.0523380i
$966$		0			0
$967$	25.5974	+	25.5974i	0.823158	+	0.823158i	0.986560	−	0.163402i	$-0.0522467\pi$
$967$	25.5974	+	25.5974i	0.823158	+	0.823158i	−0.163402	+	0.986560i	$0.552247\pi$
$968$		0			0
$969$	15.8525	−	64.7416i	0.509255	−	2.07980i
$970$		0			0
$971$	−10.9656	−	10.9656i	−0.351904	−	0.351904i	0.508914	−	0.860817i	$-0.330047\pi$
$971$	−10.9656	−	10.9656i	−0.351904	−	0.351904i	−0.860817	+	0.508914i	$0.830047\pi$
$972$		0			0
$973$		−	6.27390i		−	0.201132i
$974$		0			0
$975$	36.3493	−	87.7549i	1.16411	−	2.81041i
$976$		0			0
$977$	−32.4460	+	32.4460i	−1.03804	+	1.03804i	−0.0387927	+	0.999247i	$0.512351\pi$
$977$	−32.4460	+	32.4460i	−1.03804	+	1.03804i	−0.999247	+	0.0387927i	$0.987649\pi$
$978$		0			0
$979$	3.02583	+	1.25334i	0.0967058	+	0.0400569i
$980$		0			0
$981$	128.665	−	53.2947i	4.10795	−	1.70157i
$982$		0			0
$983$	15.0882	+	36.4260i	0.481238	+	1.16181i	0.959022	+	0.283333i	$0.0914401\pi$
$983$	15.0882	+	36.4260i	0.481238	+	1.16181i	−0.477784	+	0.878477i	$0.658560\pi$
$984$		0			0
$985$	−3.21090			−0.102308
$986$		0			0
$987$	−59.1692			−1.88338
$988$		0			0
$989$	6.75792	+	16.3151i	0.214889	+	0.518788i
$990$		0			0
$991$	−43.2501	+	17.9148i	−1.37388	+	0.569081i	−0.942839	−	0.333249i	$-0.891855\pi$
$991$	−43.2501	+	17.9148i	−1.37388	+	0.569081i	−0.431045	+	0.902330i	$0.641855\pi$
$992$		0			0
$993$	36.4190	+	15.0852i	1.15572	+	0.478716i
$994$		0			0
$995$	1.84605	−	1.84605i	0.0585239	−	0.0585239i
$996$		0			0
$997$	23.2500	−	56.1304i	0.736335	−	1.77767i	0.116122	−	0.993235i	$-0.462954\pi$
$997$	23.2500	−	56.1304i	0.736335	−	1.77767i	0.620212	−	0.784434i	$-0.287046\pi$
$998$		0			0
$999$		−	47.1335i		−	1.49124i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.2.n.c.49.1	yes	12
3.2	odd	2		1224.2.bq.c.865.2		12
4.3	odd	2		272.2.v.f.49.3		12
17.3	odd	16		2312.2.b.n.577.1		12
17.5	odd	16		2312.2.a.w.1.12		12
17.8	even	8	inner	136.2.n.c.25.1	✓	12
17.12	odd	16		2312.2.a.w.1.1		12
17.14	odd	16		2312.2.b.n.577.12		12
51.8	odd	8		1224.2.bq.c.433.2		12
68.39	even	16		4624.2.a.bt.1.1		12
68.59	odd	8		272.2.v.f.161.3		12
68.63	even	16		4624.2.a.bt.1.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.n.c.25.1	✓	12	17.8	even	8	inner
136.2.n.c.49.1	yes	12	1.1	even	1	trivial
272.2.v.f.49.3		12	4.3	odd	2
272.2.v.f.161.3		12	68.59	odd	8
1224.2.bq.c.433.2		12	51.8	odd	8
1224.2.bq.c.865.2		12	3.2	odd	2
2312.2.a.w.1.1		12	17.12	odd	16
2312.2.a.w.1.12		12	17.5	odd	16
2312.2.b.n.577.1		12	17.3	odd	16
2312.2.b.n.577.12		12	17.14	odd	16
4624.2.a.bt.1.1		12	68.39	even	16
4624.2.a.bt.1.12		12	68.63	even	16

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	136.n (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24310 - 3.00110i) q^{3} +(0.194339 - 0.0804980i) q^{5} +(-1.76317 - 0.730328i) q^{7} +(-5.33998 + 5.33998i) q^{9} +O(q^{10})\)	\(q+(-1.24310 - 3.00110i) q^{3} +(0.194339 - 0.0804980i) q^{5} +(-1.76317 - 0.730328i) q^{7} +(-5.33998 + 5.33998i) q^{9} +(0.356936 - 0.861721i) q^{11} -5.90040i q^{13} +(-0.483165 - 0.483165i) q^{15} +(4.07521 - 0.626609i) q^{17} +(3.51903 + 3.51903i) q^{19} +6.19930i q^{21} +(1.71673 - 4.14454i) q^{23} +(-3.50425 + 3.50425i) q^{25} +(13.6606 + 5.65841i) q^{27} +(6.46407 - 2.67750i) q^{29} +(-1.31309 - 3.17008i) q^{31} -3.02981 q^{33} -0.401443 q^{35} +(-1.21987 - 2.94504i) q^{37} +(-17.7077 + 7.33476i) q^{39} +(7.03058 + 2.91216i) q^{41} +(-2.78354 + 2.78354i) q^{43} +(-0.607910 + 1.46763i) q^{45} +9.54449i q^{47} +(-2.37437 - 2.37437i) q^{49} +(-6.94639 - 11.4512i) q^{51} +(2.21135 + 2.21135i) q^{53} -0.196199i q^{55} +(6.18646 - 14.9354i) q^{57} +(1.95511 - 1.95511i) q^{59} +(-0.440083 - 0.182288i) q^{61} +(13.3152 - 5.51534i) q^{63} +(-0.474971 - 1.14668i) q^{65} -4.33796 q^{67} -14.5722 q^{69} +(-0.788702 - 1.90409i) q^{71} +(0.971614 - 0.402456i) q^{73} +(14.8727 + 6.16047i) q^{75} +(-1.25868 + 1.25868i) q^{77} +(-4.85539 + 11.7219i) q^{79} -25.3751i q^{81} +(0.666789 + 0.666789i) q^{83} +(0.741534 - 0.449821i) q^{85} +(-16.0709 - 16.0709i) q^{87} +3.51138i q^{89} +(-4.30923 + 10.4034i) q^{91} +(-7.88141 + 7.88141i) q^{93} +(0.967161 + 0.400611i) q^{95} +(-2.66222 + 1.10273i) q^{97} +(2.69554 + 6.50760i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{5} - 8 q^{9}+O(q^{10}) \) 12 * q + 4 * q^5 - 8 * q^9	\( 12 q + 4 q^{5} - 8 q^{9} - 12 q^{11} + 20 q^{15} + 4 q^{17} - 4 q^{19} - 8 q^{23} - 16 q^{25} + 24 q^{27} + 8 q^{29} - 32 q^{31} - 24 q^{33} - 32 q^{35} + 4 q^{37} - 8 q^{39} + 16 q^{41} + 8 q^{43} - 64 q^{45} + 44 q^{49} - 8 q^{51} - 8 q^{53} - 12 q^{57} + 16 q^{59} + 44 q^{61} + 100 q^{63} - 20 q^{65} - 40 q^{67} + 56 q^{69} + 32 q^{71} + 8 q^{73} + 92 q^{75} - 12 q^{77} - 8 q^{79} + 40 q^{83} + 40 q^{85} - 84 q^{87} - 40 q^{91} - 76 q^{93} + 28 q^{95} - 16 q^{97} - 68 q^{99}+O(q^{100}) \) 12 * q + 4 * q^5 - 8 * q^9 - 12 * q^11 + 20 * q^15 + 4 * q^17 - 4 * q^19 - 8 * q^23 - 16 * q^25 + 24 * q^27 + 8 * q^29 - 32 * q^31 - 24 * q^33 - 32 * q^35 + 4 * q^37 - 8 * q^39 + 16 * q^41 + 8 * q^43 - 64 * q^45 + 44 * q^49 - 8 * q^51 - 8 * q^53 - 12 * q^57 + 16 * q^59 + 44 * q^61 + 100 * q^63 - 20 * q^65 - 40 * q^67 + 56 * q^69 + 32 * q^71 + 8 * q^73 + 92 * q^75 - 12 * q^77 - 8 * q^79 + 40 * q^83 + 40 * q^85 - 84 * q^87 - 40 * q^91 - 76 * q^93 + 28 * q^95 - 16 * q^97 - 68 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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