LMFDB - Embedded newform 684.2.f.b.379.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(379,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("684.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.f (of order $2$, degree $1$, 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:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.14453810176.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 6x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 6x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 76)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.3
Root			$-0.331077 - 1.37491i$ of defining polynomial
Character	$\chi$	$=$	684.379
Dual form			684.2.f.b.379.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.331077 - 1.37491i) q^{2} +(-1.78078 + 0.910404i) q^{4} +2.56155 q^{5} -4.15286i q^{7} +(1.84130 + 2.14700i) q^{8} +O(q^{10})$	\(q+(-0.331077 - 1.37491i) q^{2} +(-1.78078 + 0.910404i) q^{4} +2.56155 q^{5} -4.15286i q^{7} +(1.84130 + 2.14700i) q^{8} +(-0.848071 - 3.52191i) q^{10} -2.33205i q^{11} +4.29400i q^{13} +(-5.70982 + 1.37491i) q^{14} +(2.34233 - 3.24245i) q^{16} +1.00000 q^{17} +(3.68260 - 2.33205i) q^{19} +(-4.56155 + 2.33205i) q^{20} +(-3.20636 + 0.772087i) q^{22} -1.82081i q^{23} +1.56155 q^{25} +(5.90388 - 1.42164i) q^{26} +(3.78078 + 7.39531i) q^{28} -1.20565i q^{29} -1.32431 q^{31} +(-5.23358 - 2.14700i) q^{32} +(-0.331077 - 1.37491i) q^{34} -10.6378i q^{35} -5.49966i q^{37} +(-4.42559 - 4.29117i) q^{38} +(4.71659 + 5.49966i) q^{40} -5.49966i q^{41} -1.30957i q^{43} +(2.12311 + 4.15286i) q^{44} +(-2.50345 + 0.602827i) q^{46} +6.99614i q^{47} -10.2462 q^{49} +(-0.516994 - 2.14700i) q^{50} +(-3.90928 - 7.64666i) q^{52} -9.79366i q^{53} -5.97366i q^{55} +(8.91618 - 7.64666i) q^{56} +(-1.65767 + 0.399164i) q^{58} -6.33122 q^{59} +11.6847 q^{61} +(0.438447 + 1.82081i) q^{62} +(-1.21922 + 7.90655i) q^{64} +10.9993i q^{65} -0.290319 q^{67} +(-1.78078 + 0.910404i) q^{68} +(-14.6260 + 3.52191i) q^{70} -2.06798 q^{71} -0.123106 q^{73} +(-7.56155 + 1.82081i) q^{74} +(-4.43478 + 7.50551i) q^{76} -9.68466 q^{77} -13.4061 q^{79} +(6.00000 - 8.30571i) q^{80} +(-7.56155 + 1.82081i) q^{82} +11.9473i q^{83} +2.56155 q^{85} +(-1.80054 + 0.433567i) q^{86} +(5.00691 - 4.29400i) q^{88} +14.0877i q^{89} +17.8324 q^{91} +(1.65767 + 3.24245i) q^{92} +(9.61909 - 2.31626i) q^{94} +(9.43318 - 5.97366i) q^{95} -2.41131i q^{97} +(3.39228 + 14.0877i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{4} + 4 q^{5}+O(q^{10}) $ 8 * q - 6 * q^4 + 4 * q^5	$ 8 q - 6 q^{4} + 4 q^{5} - 6 q^{16} + 8 q^{17} - 20 q^{20} - 4 q^{25} + 6 q^{26} + 22 q^{28} - 18 q^{38} - 16 q^{44} - 16 q^{49} - 38 q^{58} + 44 q^{61} + 20 q^{62} - 18 q^{64} - 6 q^{68} + 32 q^{73} - 44 q^{74} - 16 q^{76} - 28 q^{77} + 48 q^{80} - 44 q^{82} + 4 q^{85} + 38 q^{92}+O(q^{100}) $ 8 * q - 6 * q^4 + 4 * q^5 - 6 * q^16 + 8 * q^17 - 20 * q^20 - 4 * q^25 + 6 * q^26 + 22 * q^28 - 18 * q^38 - 16 * q^44 - 16 * q^49 - 38 * q^58 + 44 * q^61 + 20 * q^62 - 18 * q^64 - 6 * q^68 + 32 * q^73 - 44 * q^74 - 16 * q^76 - 28 * q^77 + 48 * q^80 - 44 * q^82 + 4 * q^85 + 38 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.331077	−	1.37491i	−0.234107	−	0.972211i
$2$	−0.331077	−	1.37491i	−0.234107	−	0.972211i
$3$		0			0
$3$		0			0
$4$	−1.78078	+	0.910404i	−0.890388	+	0.455202i
$5$	2.56155			1.14556			0.572781	−	0.819709i	$-0.305865\pi$
$5$	2.56155			1.14556			0.572781	+	0.819709i	$0.305865\pi$
$6$		0			0
$7$		−	4.15286i		−	1.56963i	−0.619729	−	0.784816i	$-0.712757\pi$
$7$		−	4.15286i		−	1.56963i	0.619729	−	0.784816i	$-0.287243\pi$
$8$	1.84130	+	2.14700i	0.650998	+	0.759079i
$9$		0			0
$10$	−0.848071	−	3.52191i	−0.268183	−	1.11373i
$11$		−	2.33205i		−	0.703139i	−0.936162	−	0.351569i	$-0.885648\pi$
$11$		−	2.33205i		−	0.703139i	0.936162	−	0.351569i	$-0.114352\pi$
$12$		0			0
$13$			4.29400i			1.19094i	0.803377	+	0.595471i	$0.203034\pi$
$13$			4.29400i			1.19094i	−0.803377	+	0.595471i	$0.796966\pi$
$14$	−5.70982	+	1.37491i	−1.52601	+	0.367461i
$15$		0			0
$16$	2.34233	−	3.24245i	0.585582	−	0.810613i
$17$	1.00000			0.242536			0.121268	−	0.992620i	$-0.461304\pi$
$17$	1.00000			0.242536			0.121268	+	0.992620i	$0.461304\pi$
$18$		0			0
$19$	3.68260	−	2.33205i	0.844847	−	0.535008i
$19$	3.68260	−	2.33205i	0.844847	−	0.535008i
$20$	−4.56155	+	2.33205i	−1.01999	+	0.521462i
$21$		0			0
$22$	−3.20636	+	0.772087i	−0.683599	+	0.164609i
$23$		−	1.82081i		−	0.379665i	−0.981817	−	0.189832i	$-0.939206\pi$
$23$		−	1.82081i		−	0.379665i	0.981817	−	0.189832i	$-0.0607944\pi$
$24$		0			0
$25$	1.56155			0.312311
$26$	5.90388	−	1.42164i	1.15785	−	0.278807i
$27$		0			0
$28$	3.78078	+	7.39531i	0.714500	+	1.39758i
$29$		−	1.20565i		−	0.223884i	−0.993715	−	0.111942i	$-0.964293\pi$
$29$		−	1.20565i		−	0.223884i	0.993715	−	0.111942i	$-0.0357071\pi$
$30$		0			0
$31$	−1.32431			−0.237853			−0.118926	−	0.992903i	$-0.537945\pi$
$31$	−1.32431			−0.237853			−0.118926	+	0.992903i	$0.537945\pi$
$32$	−5.23358	−	2.14700i	−0.925175	−	0.379540i
$33$		0			0
$34$	−0.331077	−	1.37491i	−0.0567792	−	0.235796i
$35$		−	10.6378i		−	1.79811i
$36$		0			0
$37$		−	5.49966i		−	0.904138i	−0.891983	−	0.452069i	$-0.850686\pi$
$37$		−	5.49966i		−	0.904138i	0.891983	−	0.452069i	$-0.149314\pi$
$38$	−4.42559	−	4.29117i	−0.717925	−	0.696120i
$39$		0			0
$40$	4.71659	+	5.49966i	0.745758	+	0.869572i
$41$		−	5.49966i		−	0.858902i	−0.903090	−	0.429451i	$-0.858707\pi$
$41$		−	5.49966i		−	0.858902i	0.903090	−	0.429451i	$-0.141293\pi$
$42$		0			0
$43$		−	1.30957i		−	0.199707i	−0.995002	−	0.0998536i	$-0.968163\pi$
$43$		−	1.30957i		−	0.199707i	0.995002	−	0.0998536i	$-0.0318375\pi$
$44$	2.12311	+	4.15286i	0.320070	+	0.626067i
$45$		0			0
$46$	−2.50345	+	0.602827i	−0.369114	+	0.0888820i
$47$			6.99614i			1.02049i	0.860028	+	0.510246i	$0.170446\pi$
$47$			6.99614i			1.02049i	−0.860028	+	0.510246i	$0.829554\pi$
$48$		0			0
$49$	−10.2462			−1.46374
$50$	−0.516994	−	2.14700i	−0.0731140	−	0.303632i
$51$		0			0
$52$	−3.90928	−	7.64666i	−0.542119	−	1.06040i
$53$		−	9.79366i		−	1.34526i	−0.739978	−	0.672631i	$-0.765164\pi$
$53$		−	9.79366i		−	1.34526i	0.739978	−	0.672631i	$-0.234836\pi$
$54$		0			0
$55$		−	5.97366i		−	0.805489i
$56$	8.91618	−	7.64666i	1.19148	−	1.02183i
$57$		0			0
$58$	−1.65767	+	0.399164i	−0.217663	+	0.0524128i
$59$	−6.33122			−0.824254			−0.412127	−	0.911126i	$-0.635214\pi$
$59$	−6.33122			−0.824254			−0.412127	+	0.911126i	$0.635214\pi$
$60$		0			0
$61$	11.6847			1.49607			0.748034	−	0.663661i	$-0.230998\pi$
$61$	11.6847			1.49607			0.748034	+	0.663661i	$0.230998\pi$
$62$	0.438447	+	1.82081i	0.0556828	+	0.231243i
$63$		0			0
$64$	−1.21922	+	7.90655i	−0.152403	+	0.988318i
$65$			10.9993i			1.36430i
$66$		0			0
$67$	−0.290319			−0.0354681			−0.0177341	−	0.999843i	$-0.505645\pi$
$67$	−0.290319			−0.0354681			−0.0177341	+	0.999843i	$0.505645\pi$
$68$	−1.78078	+	0.910404i	−0.215951	+	0.110403i
$69$		0			0
$70$	−14.6260	+	3.52191i	−1.74814	+	0.420949i
$71$	−2.06798			−0.245423			−0.122712	−	0.992442i	$-0.539159\pi$
$71$	−2.06798			−0.245423			−0.122712	+	0.992442i	$0.539159\pi$
$72$		0			0
$73$	−0.123106			−0.0144084			−0.00720421	−	0.999974i	$-0.502293\pi$
$73$	−0.123106			−0.0144084			−0.00720421	+	0.999974i	$0.502293\pi$
$74$	−7.56155	+	1.82081i	−0.879013	+	0.211665i
$75$		0			0
$76$	−4.43478	+	7.50551i	−0.508705	+	0.860941i
$77$	−9.68466			−1.10367
$78$		0			0
$79$	−13.4061			−1.50830			−0.754152	−	0.656700i	$-0.771952\pi$
$79$	−13.4061			−1.50830			−0.754152	+	0.656700i	$0.771952\pi$
$80$	6.00000	−	8.30571i	0.670820	−	0.928607i
$81$		0			0
$82$	−7.56155	+	1.82081i	−0.835034	+	0.201075i
$83$			11.9473i			1.31139i	0.755026	+	0.655695i	$0.227624\pi$
$83$			11.9473i			1.31139i	−0.755026	+	0.655695i	$0.772376\pi$
$84$		0			0
$85$	2.56155			0.277839
$86$	−1.80054	+	0.433567i	−0.194158	+	0.0467528i
$87$		0			0
$88$	5.00691	−	4.29400i	0.533738	−	0.457742i
$89$			14.0877i			1.49329i	0.665223	+	0.746644i	$0.268336\pi$
$89$			14.0877i			1.49329i	−0.665223	+	0.746644i	$0.731664\pi$
$90$		0			0
$91$	17.8324			1.86934
$92$	1.65767	+	3.24245i	0.172824	+	0.338049i
$93$		0			0
$94$	9.61909	−	2.31626i	0.992134	−	0.238904i
$95$	9.43318	−	5.97366i	0.967824	−	0.612885i
$96$		0			0
$97$		−	2.41131i		−	0.244831i	−0.992479	−	0.122416i	$-0.960936\pi$
$97$		−	2.41131i		−	0.244831i	0.992479	−	0.122416i	$-0.0390641\pi$
$98$	3.39228	+	14.0877i	0.342672	+	1.42307i
$99$		0			0
$100$	−2.78078	+	1.42164i	−0.278078	+	0.142164i
$101$	8.24621			0.820529			0.410264	−	0.911967i	$-0.365436\pi$
$101$	8.24621			0.820529			0.410264	+	0.911967i	$0.365436\pi$
$102$		0			0
$103$	12.0818			1.19045			0.595227	−	0.803557i	$-0.297062\pi$
$103$	12.0818			1.19045			0.595227	+	0.803557i	$0.297062\pi$
$104$	−9.21922	+	7.90655i	−0.904019	+	0.775301i
$105$		0			0
$106$	−13.4654	+	3.24245i	−1.30788	+	0.314935i
$107$	5.75058			0.555929			0.277965	−	0.960591i	$-0.410340\pi$
$107$	5.75058			0.555929			0.277965	+	0.960591i	$0.410340\pi$
$108$		0			0
$109$			12.2050i			1.16902i	0.811385	+	0.584512i	$0.198714\pi$
$109$			12.2050i			1.16902i	−0.811385	+	0.584512i	$0.801286\pi$
$110$	−8.21327	+	1.97774i	−0.783105	+	0.188570i
$111$		0			0
$112$	−13.4654	−	9.72736i	−1.27236	−	0.919149i
$113$			5.49966i			0.517364i	0.965963	+	0.258682i	$0.0832882\pi$
$113$			5.49966i			0.517364i	−0.965963	+	0.258682i	$0.916712\pi$
$114$		0			0
$115$		−	4.66410i		−	0.434929i
$116$	1.09763	+	2.14700i	0.101913	+	0.199344i
$117$		0			0
$118$	2.09612	+	8.70488i	0.192963	+	0.801349i
$119$		−	4.15286i		−	0.380692i
$120$		0			0
$121$	5.56155			0.505596
$122$	−3.86852	−	16.0654i	−0.350239	−	1.45449i
$123$		0			0
$124$	2.35829	−	1.20565i	0.211781	−	0.108271i
$125$	−8.80776			−0.787790
$126$		0			0
$127$	6.04090			0.536043			0.268021	−	0.963413i	$-0.413630\pi$
$127$	6.04090			0.536043			0.268021	+	0.963413i	$0.413630\pi$
$128$	11.2745	−	0.941346i	0.996533	−	0.0832041i
$129$		0			0
$130$	15.1231	−	3.64162i	1.32638	−	0.319391i
$131$		−	5.97366i		−	0.521921i	−0.965349	−	0.260961i	$-0.915961\pi$
$131$		−	5.97366i		−	0.521921i	0.965349	−	0.260961i	$-0.0840393\pi$
$132$		0			0
$133$	−9.68466	−	15.2933i	−0.839766	−	1.32610i
$134$	0.0961180	+	0.399164i	0.00830333	+	0.0344825i
$135$		0			0
$136$	1.84130	+	2.14700i	0.157890	+	0.184104i
$137$	12.1231			1.03575			0.517873	−	0.855457i	$-0.326724\pi$
$137$	12.1231			1.03575			0.517873	+	0.855457i	$0.326724\pi$
$138$		0			0
$139$			18.9435i			1.60676i	0.595464	+	0.803382i	$0.296968\pi$
$139$			18.9435i			1.60676i	−0.595464	+	0.803382i	$0.703032\pi$
$140$	9.68466	+	18.9435i	0.818503	+	1.60102i
$141$		0			0
$142$	0.684658	+	2.84329i	0.0574553	+	0.238603i
$143$	10.0138			0.837397
$144$		0			0
$145$		−	3.08835i		−	0.256473i
$146$	0.0407574	+	0.169260i	0.00337311	+	0.0140080i
$147$		0			0
$148$	5.00691	+	9.79366i	0.411565	+	0.805034i
$149$	−2.80776			−0.230021			−0.115010	−	0.993364i	$-0.536690\pi$
$149$	−2.80776			−0.230021			−0.115010	+	0.993364i	$0.536690\pi$
$150$		0			0
$151$	−8.85254			−0.720409			−0.360205	−	0.932873i	$-0.617293\pi$
$151$	−8.85254			−0.720409			−0.360205	+	0.932873i	$0.617293\pi$
$152$	11.7877	+	3.61255i	0.956107	+	0.293016i
$153$		0			0
$154$	3.20636	+	13.3156i	0.258376	+	1.07300i
$155$	−3.39228			−0.272475
$156$		0			0
$157$	6.00000			0.478852			0.239426	−	0.970915i	$-0.423041\pi$
$157$	6.00000			0.478852			0.239426	+	0.970915i	$0.423041\pi$
$158$	4.43845	+	18.4322i	0.353104	+	1.46639i
$159$		0			0
$160$	−13.4061	−	5.49966i	−1.05985	−	0.434786i
$161$	−7.56155			−0.595934
$162$		0			0
$163$		−	17.6339i		−	1.38119i	−0.723240	−	0.690597i	$-0.757348\pi$
$163$		−	17.6339i		−	1.38119i	0.723240	−	0.690597i	$-0.242652\pi$
$164$	5.00691	+	9.79366i	0.390974	+	0.764756i
$165$		0			0
$166$	16.4265	−	3.95548i	1.27495	−	0.307005i
$167$	10.7575			0.832439			0.416220	−	0.909264i	$-0.363355\pi$
$167$	10.7575			0.832439			0.416220	+	0.909264i	$0.363355\pi$
$168$		0			0
$169$	−5.43845			−0.418342
$170$	−0.848071	−	3.52191i	−0.0650440	−	0.270119i
$171$		0			0
$172$	1.19224	+	2.33205i	0.0909071	+	0.177817i
$173$			2.41131i			0.183328i	0.995790	+	0.0916642i	$0.0292186\pi$
$173$			2.41131i			0.183328i	−0.995790	+	0.0916642i	$0.970781\pi$
$174$		0			0
$175$		−	6.48490i		−	0.490213i
$176$	−7.56155	−	5.46242i	−0.569973	−	0.411746i
$177$		0			0
$178$	19.3693	−	4.66410i	1.45179	−	0.349589i
$179$	8.10887			0.606085			0.303043	−	0.952977i	$-0.401998\pi$
$179$	8.10887			0.606085			0.303043	+	0.952977i	$0.401998\pi$
$180$		0			0
$181$			19.5873i			1.45591i	0.685623	+	0.727957i	$0.259530\pi$
$181$			19.5873i			1.45591i	−0.685623	+	0.727957i	$0.740470\pi$
$182$	−5.90388	−	24.5180i	−0.437625	−	1.81739i
$183$		0			0
$184$	3.90928	−	3.35265i	0.288196	−	0.247161i
$185$		−	14.0877i		−	1.03575i
$186$		0			0
$187$		−	2.33205i		−	0.170536i
$188$	−6.36932	−	12.4586i	−0.464530	−	0.908634i
$189$		0			0
$190$	−11.3364	−	10.9921i	−0.822427	−	0.797448i
$191$			7.79447i			0.563988i	0.959416	+	0.281994i	$0.0909959\pi$
$191$			7.79447i			0.563988i	−0.959416	+	0.281994i	$0.909004\pi$
$192$		0			0
$193$			5.49966i			0.395874i	0.980215	+	0.197937i	$0.0634241\pi$
$193$			5.49966i			0.395874i	−0.980215	+	0.197937i	$0.936576\pi$
$194$	−3.31534	+	0.798328i	−0.238028	+	0.0573166i
$195$		0			0
$196$	18.2462	−	9.32819i	1.30330	−	0.666299i
$197$	22.4924			1.60252			0.801259	−	0.598317i	$-0.204164\pi$
$197$	22.4924			1.60252			0.801259	+	0.598317i	$0.204164\pi$
$198$		0			0
$199$			5.17534i			0.366870i	0.983032	+	0.183435i	$0.0587217\pi$
$199$			5.17534i			0.366870i	−0.983032	+	0.183435i	$0.941278\pi$
$200$	2.87529	+	3.35265i	0.203314	+	0.237069i
$201$		0			0
$202$	−2.73013	−	11.3378i	−0.192091	−	0.797727i
$203$	−5.00691			−0.351416
$204$		0			0
$205$		−	14.0877i		−	0.983925i
$206$	−4.00000	−	16.6114i	−0.278693	−	1.15737i
$207$		0			0
$208$	13.9231	+	10.0580i	0.965393	+	0.697394i
$209$	−5.43845	−	8.58800i	−0.376185	−	0.594045i
$210$		0			0
$211$	−25.1976			−1.73467			−0.867336	−	0.497723i	$-0.834170\pi$
$211$	−25.1976			−1.73467			−0.867336	+	0.497723i	$0.834170\pi$
$212$	8.91618	+	17.4403i	0.612366	+	1.19781i
$213$		0			0
$214$	−1.90388	−	7.90655i	−0.130147	−	0.540480i
$215$		−	3.35453i		−	0.228777i
$216$		0			0
$217$			5.49966i			0.373341i
$218$	16.7808	−	4.04078i	1.13654	−	0.273676i
$219$		0			0
$220$	5.43845	+	10.6378i	0.366660	+	0.717198i
$221$			4.29400i			0.288846i
$222$		0			0
$223$	22.2586			1.49055			0.745274	−	0.666758i	$-0.232319\pi$
$223$	22.2586			1.49055			0.745274	+	0.666758i	$0.232319\pi$
$224$	−8.91618	+	21.7343i	−0.595738	+	1.45218i
$225$		0			0
$226$	7.56155	−	1.82081i	0.502987	−	0.121118i
$227$	−24.6169			−1.63388			−0.816942	−	0.576720i	$-0.804332\pi$
$227$	−24.6169			−1.63388			−0.816942	+	0.576720i	$0.804332\pi$
$228$		0			0
$229$	−6.56155			−0.433600			−0.216800	−	0.976216i	$-0.569562\pi$
$229$	−6.56155			−0.433600			−0.216800	+	0.976216i	$0.569562\pi$
$230$	−6.41273	+	1.54417i	−0.422843	+	0.101820i
$231$		0			0
$232$	2.58854	−	2.21997i	0.169946	−	0.145748i
$233$	−10.8078			−0.708040			−0.354020	−	0.935238i	$-0.615186\pi$
$233$	−10.8078			−0.708040			−0.354020	+	0.935238i	$0.615186\pi$
$234$		0			0
$235$			17.9210i			1.16904i
$236$	11.2745	−	5.76396i	0.733906	−	0.375202i
$237$		0			0
$238$	−5.70982	+	1.37491i	−0.370113	+	0.0891224i
$239$			9.83943i			0.636460i	0.948014	+	0.318230i	$0.103088\pi$
$239$			9.83943i			0.636460i	−0.948014	+	0.318230i	$0.896912\pi$
$240$		0			0
$241$			22.6757i			1.46067i	0.683090	+	0.730334i	$0.260635\pi$
$241$			22.6757i			1.46067i	−0.683090	+	0.730334i	$0.739365\pi$
$242$	−1.84130	−	7.64666i	−0.118363	−	0.491546i
$243$		0			0
$244$	−20.8078	+	10.6378i	−1.33208	+	0.681013i
$245$	−26.2462			−1.67681
$246$		0			0
$247$	10.0138	+	15.8131i	0.637164	+	1.00616i
$248$	−2.43845	−	2.84329i	−0.154842	−	0.180549i
$249$		0			0
$250$	2.91605	+	12.1099i	0.184427	+	0.765898i
$251$			21.5626i			1.36102i	0.732739	+	0.680510i	$0.238242\pi$
$251$			21.5626i			1.36102i	−0.732739	+	0.680510i	$0.761758\pi$
$252$		0			0
$253$	−4.24621			−0.266957
$254$	−2.00000	−	8.30571i	−0.125491	−	0.521147i
$255$		0			0
$256$	−5.02699	−	15.1898i	−0.314187	−	0.949361i
$257$			17.1760i			1.07141i	0.844405	+	0.535705i	$0.179954\pi$
$257$			17.1760i			1.07141i	−0.844405	+	0.535705i	$0.820046\pi$
$258$		0			0
$259$	−22.8393			−1.41916
$260$	−10.0138	−	19.5873i	−0.621031	−	1.21475i
$261$		0			0
$262$	−8.21327	+	1.97774i	−0.507418	+	0.122185i
$263$			14.2794i			0.880504i	0.897874	+	0.440252i	$0.145111\pi$
$263$			14.2794i			0.880504i	−0.897874	+	0.440252i	$0.854889\pi$
$264$		0			0
$265$		−	25.0870i		−	1.54108i
$266$	−17.8206	+	18.3788i	−1.09265	+	1.12688i
$267$		0			0
$268$	0.516994	−	0.264308i	0.0315804	−	0.0161452i
$269$		−	5.49966i		−	0.335320i	−0.985845	−	0.167660i	$-0.946379\pi$
$269$		−	5.49966i		−	0.335320i	0.985845	−	0.167660i	$-0.0536211\pi$
$270$		0			0
$271$			22.0738i			1.34089i	0.741959	+	0.670445i	$0.233897\pi$
$271$			22.0738i			1.34089i	−0.741959	+	0.670445i	$0.766103\pi$
$272$	2.34233	−	3.24245i	0.142025	−	0.196603i
$273$		0			0
$274$	−4.01368	−	16.6682i	−0.242475	−	1.00696i
$275$		−	3.64162i		−	0.219598i
$276$		0			0
$277$	13.0540			0.784337			0.392169	−	0.919893i	$-0.371725\pi$
$277$	13.0540			0.784337			0.392169	+	0.919893i	$0.371725\pi$
$278$	26.0456	−	6.27174i	1.56211	−	0.376154i
$279$		0			0
$280$	22.8393	−	19.5873i	1.36491	−	1.17057i
$281$		−	28.1753i		−	1.68080i	−0.541968	−	0.840399i	$-0.682321\pi$
$281$		−	28.1753i		−	1.68080i	0.541968	−	0.840399i	$-0.317679\pi$
$282$		0			0
$283$			5.97366i			0.355097i	0.984112	+	0.177549i	$0.0568167\pi$
$283$			5.97366i			0.355097i	−0.984112	+	0.177549i	$0.943183\pi$
$284$	3.68260	−	1.88269i	0.218522	−	0.111717i
$285$		0			0
$286$	−3.31534	−	13.7681i	−0.196040	−	0.814127i
$287$	−22.8393			−1.34816
$288$		0			0
$289$	−16.0000			−0.941176
$290$	−4.24621	+	1.02248i	−0.249346	+	0.0600421i
$291$		0			0
$292$	0.219224	−	0.112076i	0.0128291	−	0.00655874i
$293$			4.29400i			0.250858i	0.992103	+	0.125429i	$0.0400308\pi$
$293$			4.29400i			0.250858i	−0.992103	+	0.125429i	$0.959969\pi$
$294$		0			0
$295$	−16.2177			−0.944233
$296$	11.8078	−	10.1265i	0.686312	−	0.588592i
$297$		0			0
$298$	0.929585	+	3.86043i	0.0538494	+	0.223629i
$299$	7.81855			0.452159
$300$		0			0
$301$	−5.43845			−0.313467
$302$	2.93087	+	12.1715i	0.168653	+	0.700390i
$303$		0			0
$304$	1.06431	−	17.4031i	0.0610425	−	0.998135i
$305$	29.9309			1.71384
$306$		0			0
$307$	−13.4061			−0.765126			−0.382563	−	0.923929i	$-0.624959\pi$
$307$	−13.4061			−0.765126			−0.382563	+	0.923929i	$0.624959\pi$
$308$	17.2462	−	8.81695i	0.982694	−	0.502392i
$309$		0			0
$310$	1.12311	+	4.66410i	0.0637881	+	0.264903i
$311$			4.15286i			0.235487i	0.993044	+	0.117743i	$0.0375660\pi$
$311$			4.15286i			0.235487i	−0.993044	+	0.117743i	$0.962434\pi$
$312$		0			0
$313$	−0.438447			−0.0247825			−0.0123913	−	0.999923i	$-0.503944\pi$
$313$	−0.438447			−0.0247825			−0.0123913	+	0.999923i	$0.503944\pi$
$314$	−1.98646	−	8.24948i	−0.112102	−	0.465545i
$315$		0			0
$316$	23.8733	−	12.2050i	1.34298	−	0.686583i
$317$		−	4.29400i		−	0.241175i	−0.992703	−	0.120588i	$-0.961522\pi$
$317$		−	4.29400i		−	0.241175i	0.992703	−	0.120588i	$-0.0384779\pi$
$318$		0			0
$319$	−2.81164			−0.157422
$320$	−3.12311	+	20.2530i	−0.174587	+	1.13218i
$321$		0			0
$322$	2.50345	+	10.3965i	0.139512	+	0.579373i
$323$	3.68260	−	2.33205i	0.204905	−	0.129759i
$324$		0			0
$325$			6.70531i			0.371944i
$326$	−24.2451	+	5.83817i	−1.34281	+	0.323347i
$327$		0			0
$328$	11.8078	−	10.1265i	0.651975	−	0.559144i
$329$	29.0540			1.60180
$330$		0			0
$331$	−23.8733			−1.31219			−0.656097	−	0.754677i	$-0.727794\pi$
$331$	−23.8733			−1.31219			−0.656097	+	0.754677i	$0.727794\pi$
$332$	−10.8769	−	21.2755i	−0.596947	−	1.16765i
$333$		0			0
$334$	−3.56155	−	14.7906i	−0.194879	−	0.809306i
$335$	−0.743668			−0.0406309
$336$		0			0
$337$		−	6.17669i		−	0.336466i	−0.985747	−	0.168233i	$-0.946194\pi$
$337$		−	6.17669i		−	0.336466i	0.985747	−	0.168233i	$-0.0538061\pi$
$338$	1.80054	+	7.47740i	0.0979366	+	0.406717i
$339$		0			0
$340$	−4.56155	+	2.33205i	−0.247385	+	0.126473i
$341$			3.08835i			0.167243i
$342$		0			0
$343$			13.4810i			0.727908i
$344$	2.81164	−	2.41131i	0.151594	−	0.130009i
$345$		0			0
$346$	3.31534	−	0.798328i	0.178234	−	0.0429184i
$347$		−	29.8683i		−	1.60342i	−0.597716	−	0.801708i	$-0.703925\pi$
$347$		−	29.8683i		−	1.60342i	0.597716	−	0.801708i	$-0.296075\pi$
$348$		0			0
$349$	9.05398			0.484648			0.242324	−	0.970195i	$-0.422090\pi$
$349$	9.05398			0.484648			0.242324	+	0.970195i	$0.422090\pi$
$350$	−8.91618	+	2.14700i	−0.476590	+	0.114762i
$351$		0			0
$352$	−5.00691	+	12.2050i	−0.266869	+	0.650527i
$353$	−18.6847			−0.994484			−0.497242	−	0.867612i	$-0.665654\pi$
$353$	−18.6847			−0.994484			−0.497242	+	0.867612i	$0.665654\pi$
$354$		0			0
$355$	−5.29723			−0.281148
$356$	−12.8255	−	25.0870i	−0.679748	−	1.32961i
$357$		0			0
$358$	−2.68466	−	11.1490i	−0.141889	−	0.589243i
$359$			6.19782i			0.327108i	0.986534	+	0.163554i	$0.0522958\pi$
$359$			6.19782i			0.327108i	−0.986534	+	0.163554i	$0.947704\pi$
$360$		0			0
$361$	8.12311	−	17.1760i	0.427532	−	0.904000i
$362$	26.9309	−	6.48490i	1.41546	−	0.340839i
$363$		0			0
$364$	−31.7555	+	16.2347i	−1.66444	+	0.850927i
$365$	−0.315342			−0.0165057
$366$		0			0
$367$		−	1.02248i		−	0.0533730i	−0.999644	−	0.0266865i	$-0.991504\pi$
$367$		−	1.02248i		−	0.0533730i	0.999644	−	0.0266865i	$-0.00849559\pi$
$368$	−5.90388	−	4.26493i	−0.307761	−	0.222325i
$369$		0			0
$370$	−19.3693	+	4.66410i	−1.00696	+	0.242475i
$371$	−40.6716			−2.11157
$372$		0			0
$373$			6.70531i			0.347188i	0.984817	+	0.173594i	$0.0555380\pi$
$373$			6.70531i			0.347188i	−0.984817	+	0.173594i	$0.944462\pi$
$374$	−3.20636	+	0.772087i	−0.165797	+	0.0399237i
$375$		0			0
$376$	−15.0207	+	12.8820i	−0.774635	+	0.664339i
$377$	5.17708			0.266633
$378$		0			0
$379$	15.7644			0.809762			0.404881	−	0.914369i	$-0.367313\pi$
$379$	15.7644			0.809762			0.404881	+	0.914369i	$0.367313\pi$
$380$	−11.3599	+	19.2258i	−0.582752	+	0.986261i
$381$		0			0
$382$	10.7167	−	2.58057i	0.548315	−	0.132033i
$383$	22.2586			1.13736			0.568682	−	0.822558i	$-0.307454\pi$
$383$	22.2586			1.13736			0.568682	+	0.822558i	$0.307454\pi$
$384$		0			0
$385$	−24.8078			−1.26432
$386$	7.56155	−	1.82081i	0.384873	−	0.0926767i
$387$		0			0
$388$	2.19526	+	4.29400i	0.111448	+	0.217995i
$389$	−14.8078			−0.750783			−0.375392	−	0.926866i	$-0.622492\pi$
$389$	−14.8078			−0.750783			−0.375392	+	0.926866i	$0.622492\pi$
$390$		0			0
$391$		−	1.82081i		−	0.0920822i
$392$	−18.8664	−	21.9986i	−0.952895	−	1.11110i
$393$		0			0
$394$	−7.44672	−	30.9251i	−0.375160	−	1.55799i
$395$	−34.3404			−1.72785
$396$		0			0
$397$	−3.93087			−0.197285			−0.0986423	−	0.995123i	$-0.531450\pi$
$397$	−3.93087			−0.197285			−0.0986423	+	0.995123i	$0.531450\pi$
$398$	7.11564	−	1.71343i	0.356675	−	0.0858866i
$399$		0			0
$400$	3.65767	−	5.06326i	0.182884	−	0.253163i
$401$		−	7.91096i		−	0.395055i	−0.980297	−	0.197527i	$-0.936709\pi$
$401$		−	7.91096i		−	0.395055i	0.980297	−	0.197527i	$-0.0632911\pi$
$402$		0			0
$403$		−	5.68658i		−	0.283269i
$404$	−14.6847	+	7.50738i	−0.730589	+	0.373506i
$405$		0			0
$406$	1.65767	+	6.88407i	0.0822688	+	0.341651i
$407$	−12.8255			−0.635734
$408$		0			0
$409$		−	27.4983i		−	1.35970i	−0.733350	−	0.679851i	$-0.762044\pi$
$409$		−	27.4983i		−	1.35970i	0.733350	−	0.679851i	$-0.237956\pi$
$410$	−19.3693	+	4.66410i	−0.956582	+	0.230343i
$411$		0			0
$412$	−21.5150	+	10.9993i	−1.05997	+	0.541897i
$413$			26.2926i			1.29378i
$414$		0			0
$415$			30.6037i			1.50228i
$416$	9.21922	−	22.4730i	0.452010	−	1.10183i
$417$		0			0
$418$	−10.0072	+	10.3207i	−0.489469	+	0.504801i
$419$		−	39.9319i		−	1.95080i	−0.220440	−	0.975401i	$-0.570749\pi$
$419$		−	39.9319i		−	1.95080i	0.220440	−	0.975401i	$-0.429251\pi$
$420$		0			0
$421$		−	23.2043i		−	1.13091i	−0.824780	−	0.565454i	$-0.808701\pi$
$421$		−	23.2043i		−	1.13091i	0.824780	−	0.565454i	$-0.191299\pi$
$422$	8.34233	+	34.6445i	0.406098	+	1.68647i
$423$		0			0
$424$	21.0270	−	18.0331i	1.02116	−	0.875763i
$425$	1.56155			0.0757464
$426$		0			0
$427$		−	48.5247i		−	2.34827i
$428$	−10.2405	+	5.23535i	−0.494993	+	0.253060i
$429$		0			0
$430$	−4.61219	+	1.11061i	−0.222419	+	0.0535582i
$431$	5.29723			0.255158			0.127579	−	0.991828i	$-0.459279\pi$
$431$	5.29723			0.255158			0.127579	+	0.991828i	$0.459279\pi$
$432$		0			0
$433$		−	18.9103i		−	0.908770i	−0.890805	−	0.454385i	$-0.849859\pi$
$433$		−	18.9103i		−	0.908770i	0.890805	−	0.454385i	$-0.150141\pi$
$434$	7.56155	−	1.82081i	0.362966	−	0.0874016i
$435$		0			0
$436$	−11.1114	−	21.7343i	−0.532142	−	1.04088i
$437$	−4.24621	−	6.70531i	−0.203124	−	0.320758i
$438$		0			0
$439$	19.6100			0.935935			0.467968	−	0.883746i	$-0.344986\pi$
$439$	19.6100			0.935935			0.467968	+	0.883746i	$0.344986\pi$
$440$	12.8255	−	10.9993i	0.611430	−	0.524372i
$441$		0			0
$442$	5.90388	−	1.42164i	0.280819	−	0.0676207i
$443$			12.2344i			0.581275i	0.956833	+	0.290637i	$0.0938673\pi$
$443$			12.2344i			0.581275i	−0.956833	+	0.290637i	$0.906133\pi$
$444$		0			0
$445$			36.0863i			1.71065i
$446$	−7.36932	−	30.6037i	−0.348947	−	1.44913i
$447$		0			0
$448$	32.8348	+	5.06326i	1.55130	+	0.239217i
$449$		−	14.7647i		−	0.696789i	−0.937348	−	0.348395i	$-0.886727\pi$
$449$		−	14.7647i		−	0.696789i	0.937348	−	0.348395i	$-0.113273\pi$
$450$		0			0
$451$	−12.8255			−0.603927
$452$	−5.00691	−	9.79366i	−0.235505	−	0.460655i
$453$		0			0
$454$	8.15009	+	33.8462i	0.382503	+	1.58848i
$455$	45.6786			2.14144
$456$		0			0
$457$	3.87689			0.181353			0.0906767	−	0.995880i	$-0.471097\pi$
$457$	3.87689			0.181353			0.0906767	+	0.995880i	$0.471097\pi$
$458$	2.17238	+	9.02157i	0.101509	+	0.421550i
$459$		0			0
$460$	4.24621	+	8.30571i	0.197981	+	0.387256i
$461$	−31.6847			−1.47570			−0.737851	−	0.674964i	$-0.764159\pi$
$461$	−31.6847			−1.47570			−0.737851	+	0.674964i	$0.764159\pi$
$462$		0			0
$463$		−	16.3243i		−	0.758656i	−0.925262	−	0.379328i	$-0.876155\pi$
$463$		−	16.3243i		−	0.758656i	0.925262	−	0.379328i	$-0.123845\pi$
$464$	−3.90928	−	2.82404i	−0.181484	−	0.131103i
$465$		0			0
$466$	3.57820	+	14.8597i	0.165757	+	0.688364i
$467$		−	2.33205i		−	0.107914i	−0.998543	−	0.0539572i	$-0.982817\pi$
$467$		−	2.33205i		−	0.107914i	0.998543	−	0.0539572i	$-0.0171834\pi$
$468$		0			0
$469$			1.20565i			0.0556719i
$470$	24.6398	−	5.93322i	1.13655	−	0.273679i
$471$		0			0
$472$	−11.6577	−	13.5931i	−0.536588	−	0.625674i
$473$	−3.05398			−0.140422
$474$		0			0
$475$	5.75058	−	3.64162i	0.263855	−	0.167089i
$476$	3.78078	+	7.39531i	0.173292	+	0.338963i
$477$		0			0
$478$	13.5284	−	3.25761i	0.618773	−	0.148999i
$479$			41.5286i			1.89749i	0.316045	+	0.948744i	$0.397645\pi$
$479$			41.5286i			1.89749i	−0.316045	+	0.948744i	$0.602355\pi$
$480$		0			0
$481$	23.6155			1.07678
$482$	31.1771	−	7.50738i	1.42008	−	0.341952i
$483$		0			0
$484$	−9.90388	+	5.06326i	−0.450176	+	0.230148i
$485$		−	6.17669i		−	0.280469i
$486$		0			0
$487$	18.8664			0.854916			0.427458	−	0.904035i	$-0.359409\pi$
$487$	18.8664			0.854916			0.427458	+	0.904035i	$0.359409\pi$
$488$	21.5150	+	25.0870i	0.973937	+	1.13563i
$489$		0			0
$490$	8.68951	+	36.0863i	0.392552	+	1.63021i
$491$		−	21.2755i		−	0.960151i	−0.877227	−	0.480075i	$-0.840609\pi$
$491$		−	21.2755i		−	0.960151i	0.877227	−	0.480075i	$-0.159391\pi$
$492$		0			0
$493$		−	1.20565i		−	0.0542999i
$494$	18.4263	−	19.0035i	0.829039	−	0.855007i
$495$		0			0
$496$	−3.10196	+	4.29400i	−0.139282	+	0.192806i
$497$			8.58800i			0.385225i
$498$		0			0
$499$		−	1.30957i		−	0.0586243i	−0.999570	−	0.0293122i	$-0.990668\pi$
$499$		−	1.30957i		−	0.0586243i	0.999570	−	0.0293122i	$-0.00933169\pi$
$500$	15.6847	−	8.01862i	0.701439	−	0.358604i
$501$		0			0
$502$	29.6467	−	7.13888i	1.32320	−	0.318624i
$503$		−	16.3873i		−	0.730672i	−0.930876	−	0.365336i	$-0.880954\pi$
$503$		−	16.3873i		−	0.730672i	0.930876	−	0.365336i	$-0.119046\pi$
$504$		0			0
$505$	21.1231			0.939966
$506$	1.40582	+	5.83817i	0.0624964	+	0.259539i
$507$		0			0
$508$	−10.7575	+	5.49966i	−0.477286	+	0.244008i
$509$			8.58800i			0.380657i	0.981721	+	0.190328i	$0.0609552\pi$
$509$			8.58800i			0.380657i	−0.981721	+	0.190328i	$0.939045\pi$
$510$		0			0
$511$			0.511240i			0.0226159i
$512$	−19.2203	+	11.9407i	−0.849426	+	0.527707i
$513$		0			0
$514$	23.6155	−	5.68658i	1.04164	−	0.250824i
$515$	30.9481			1.36374
$516$		0			0
$517$	16.3153			0.717548
$518$	7.56155	+	31.4020i	0.332236	+	1.37973i
$519$		0			0
$520$	−23.6155	+	20.2530i	−1.03561	+	0.888155i
$521$			22.6757i			0.993439i	0.867911	+	0.496719i	$0.165462\pi$
$521$			22.6757i			0.993439i	−0.867911	+	0.496719i	$0.834538\pi$
$522$		0			0
$523$	2.19526			0.0959922			0.0479961	−	0.998848i	$-0.484716\pi$
$523$	2.19526			0.0959922			0.0479961	+	0.998848i	$0.484716\pi$
$524$	5.43845	+	10.6378i	0.237580	+	0.464713i
$525$		0			0
$526$	19.6329	−	4.72757i	0.856036	−	0.206132i
$527$	−1.32431			−0.0576877
$528$		0			0
$529$	19.6847			0.855855
$530$	−34.4924	+	8.30571i	−1.49826	+	0.360777i
$531$		0			0
$532$	31.1693	+	18.4170i	1.35136	+	0.798479i
$533$	23.6155			1.02290
$534$		0			0
$535$	14.7304			0.636851
$536$	−0.534565	−	0.623316i	−0.0230897	−	0.0269231i
$537$		0			0
$538$	−7.56155	+	1.82081i	−0.326002	+	0.0785006i
$539$			23.8947i			1.02922i
$540$		0			0
$541$	−32.8078			−1.41052			−0.705258	−	0.708951i	$-0.749169\pi$
$541$	−32.8078			−1.41052			−0.705258	+	0.708951i	$0.749169\pi$
$542$	30.3496	−	7.30814i	1.30363	−	0.313911i
$543$		0			0
$544$	−5.23358	−	2.14700i	−0.224388	−	0.0920519i
$545$			31.2637i			1.33919i
$546$		0			0
$547$	0.580639			0.0248263			0.0124132	−	0.999923i	$-0.496049\pi$
$547$	0.580639			0.0248263			0.0124132	+	0.999923i	$0.496049\pi$
$548$	−21.5885	+	11.0369i	−0.922217	+	0.471474i
$549$		0			0
$550$	−5.00691	+	1.20565i	−0.213495	+	0.0514093i
$551$	−2.81164	−	4.43994i	−0.119780	−	0.189148i
$552$		0			0
$553$			55.6736i			2.36748i
$554$	−4.32187	−	17.9481i	−0.183619	−	0.762541i
$555$		0			0
$556$	−17.2462	−	33.7341i	−0.731402	−	1.43064i
$557$	−9.93087			−0.420784			−0.210392	−	0.977617i	$-0.567474\pi$
$557$	−9.93087			−0.420784			−0.210392	+	0.977617i	$0.567474\pi$
$558$		0			0
$559$	5.62329			0.237840
$560$	−34.4924	−	24.9171i	−1.45757	−	1.05294i
$561$		0			0
$562$	−38.7386	+	9.32819i	−1.63409	+	0.393486i
$563$	−21.3519			−0.899877			−0.449938	−	0.893060i	$-0.648554\pi$
$563$	−21.3519			−0.899877			−0.449938	+	0.893060i	$0.648554\pi$
$564$		0			0
$565$			14.0877i			0.592672i
$566$	8.21327	−	1.97774i	0.345230	−	0.0831307i
$567$		0			0
$568$	−3.80776	−	4.43994i	−0.159770	−	0.186296i
$569$		−	41.5859i		−	1.74337i	−0.490064	−	0.871687i	$-0.663027\pi$
$569$		−	41.5859i		−	1.74337i	0.490064	−	0.871687i	$-0.336973\pi$
$570$		0			0
$571$			15.5889i			0.652377i	0.945305	+	0.326188i	$0.105764\pi$
$571$			15.5889i			0.652377i	−0.945305	+	0.326188i	$0.894236\pi$
$572$	−17.8324	+	9.11662i	−0.745609	+	0.381185i
$573$		0			0
$574$	7.56155	+	31.4020i	0.315613	+	1.31070i
$575$		−	2.84329i		−	0.118573i
$576$		0			0
$577$	27.0000			1.12402			0.562012	−	0.827129i	$-0.310027\pi$
$577$	27.0000			1.12402			0.562012	+	0.827129i	$0.310027\pi$
$578$	5.29723	+	21.9986i	0.220336	+	0.915022i
$579$		0			0
$580$	2.81164	+	5.49966i	0.116747	+	0.228361i
$581$	49.6155			2.05840
$582$		0			0
$583$	−22.8393			−0.945906
$584$	−0.226674	−	0.264308i	−0.00937986	−	0.0109371i
$585$		0			0
$586$	5.90388	−	1.42164i	0.243887	−	0.0587276i
$587$		−	5.97366i		−	0.246559i	−0.992372	−	0.123280i	$-0.960659\pi$
$587$		−	5.97366i		−	0.246559i	0.992372	−	0.123280i	$-0.0393412\pi$
$588$		0			0
$589$	−4.87689	+	3.08835i	−0.200949	+	0.127253i
$590$	5.36932	+	22.2980i	0.221051	+	0.917994i
$591$		0			0
$592$	−17.8324	−	12.8820i	−0.732906	−	0.529447i
$593$	−12.7386			−0.523113			−0.261556	−	0.965188i	$-0.584236\pi$
$593$	−12.7386			−0.523113			−0.261556	+	0.965188i	$0.584236\pi$
$594$		0			0
$595$		−	10.6378i		−	0.436106i
$596$	5.00000	−	2.55620i	0.204808	−	0.104706i
$597$		0			0
$598$	−2.58854	−	10.7498i	−0.105853	−	0.439593i
$599$	24.9073			1.01768			0.508841	−	0.860860i	$-0.330074\pi$
$599$	24.9073			1.01768			0.508841	+	0.860860i	$0.330074\pi$
$600$		0			0
$601$			35.4092i			1.44437i	0.691698	+	0.722187i	$0.256863\pi$
$601$			35.4092i			1.44437i	−0.691698	+	0.722187i	$0.743137\pi$
$602$	1.80054	+	7.47740i	0.0733847	+	0.304756i
$603$		0			0
$604$	15.7644	−	8.05939i	0.641444	−	0.327932i
$605$	14.2462			0.579191
$606$		0			0
$607$	31.5288			1.27971			0.639857	−	0.768494i	$-0.278994\pi$
$607$	31.5288			1.27971			0.639857	+	0.768494i	$0.278994\pi$
$608$	−24.2801	+	4.29842i	−0.984688	+	0.174324i
$609$		0			0
$610$	−9.90941	−	41.1524i	−0.401220	−	1.66621i
$611$	−30.0414			−1.21535
$612$		0			0
$613$	−29.3002			−1.18342			−0.591712	−	0.806150i	$-0.701548\pi$
$613$	−29.3002			−1.18342			−0.591712	+	0.806150i	$0.701548\pi$
$614$	4.43845	+	18.4322i	0.179121	+	0.743864i
$615$		0			0
$616$	−17.8324	−	20.7930i	−0.718487	−	0.837773i
$617$	−41.5464			−1.67259			−0.836297	−	0.548276i	$-0.815284\pi$
$617$	−41.5464			−1.67259			−0.836297	+	0.548276i	$0.815284\pi$
$618$		0			0
$619$			6.70906i			0.269660i	0.990869	+	0.134830i	$0.0430488\pi$
$619$			6.70906i			0.269660i	−0.990869	+	0.134830i	$0.956951\pi$
$620$	6.04090	−	3.08835i	0.242608	−	0.124031i
$621$		0			0
$622$	5.70982	−	1.37491i	0.228943	−	0.0551290i
$623$	58.5040			2.34391
$624$		0			0
$625$	−30.3693			−1.21477
$626$	0.145160	+	0.602827i	0.00580175	+	0.0240938i
$627$		0			0
$628$	−10.6847	+	5.46242i	−0.426364	+	0.217974i
$629$		−	5.49966i		−	0.219286i
$630$		0			0
$631$			9.61528i			0.382778i	0.981514	+	0.191389i	$0.0612992\pi$
$631$			9.61528i			0.382778i	−0.981514	+	0.191389i	$0.938701\pi$
$632$	−24.6847	−	28.7829i	−0.981903	−	1.14492i
$633$		0			0
$634$	−5.90388	+	1.42164i	−0.234473	+	0.0564607i
$635$	15.4741			0.614070
$636$		0			0
$637$		−	43.9972i		−	1.74323i
$638$	0.930870	+	3.86577i	0.0368535	+	0.153047i
$639$		0			0
$640$	28.8802	−	2.41131i	1.14159	−	0.0953153i
$641$			26.8212i			1.05938i	0.848193	+	0.529688i	$0.177691\pi$
$641$			26.8212i			1.05938i	−0.848193	+	0.529688i	$0.822309\pi$
$642$		0			0
$643$		−	14.2794i		−	0.563124i	−0.959543	−	0.281562i	$-0.909148\pi$
$643$		−	14.2794i		−	0.563124i	0.959543	−	0.281562i	$-0.0908524\pi$
$644$	13.4654	−	6.88407i	0.530612	−	0.271270i
$645$		0			0
$646$	−4.42559	−	4.29117i	−0.174122	−	0.168834i
$647$			32.1374i			1.26345i	0.775191	+	0.631726i	$0.217653\pi$
$647$			32.1374i			1.26345i	−0.775191	+	0.631726i	$0.782347\pi$
$648$		0			0
$649$			14.7647i			0.579565i
$650$	9.21922	−	2.21997i	0.361608	−	0.0870745i
$651$		0			0
$652$	16.0540	+	31.4020i	0.628722	+	1.22980i
$653$	25.1922			0.985848			0.492924	−	0.870072i	$-0.335928\pi$
$653$	25.1922			0.985848			0.492924	+	0.870072i	$0.335928\pi$
$654$		0			0
$655$		−	15.3019i		−	0.597893i
$656$	−17.8324	−	12.8820i	−0.696237	−	0.502958i
$657$		0			0
$658$	−9.61909	−	39.9467i	−0.374991	−	1.55729i
$659$	−41.9960			−1.63593			−0.817965	−	0.575268i	$-0.804898\pi$
$659$	−41.9960			−1.63593			−0.817965	+	0.575268i	$0.804898\pi$
$660$		0			0
$661$		−	37.2919i		−	1.45049i	−0.688492	−	0.725244i	$-0.741727\pi$
$661$		−	37.2919i		−	1.45049i	0.688492	−	0.725244i	$-0.258273\pi$
$662$	7.90388	+	32.8237i	0.307193	+	1.27573i
$663$		0			0
$664$	−25.6509	+	21.9986i	−0.995449	+	0.853712i
$665$	−24.8078	−	39.1746i	−0.962004	−	1.51913i
$666$		0			0
$667$	−2.19526			−0.0850010
$668$	−19.1567	+	9.79366i	−0.741194	+	0.378928i
$669$		0			0
$670$	0.246211	+	1.02248i	0.00951197	+	0.0395018i
$671$		−	27.2492i		−	1.05194i
$672$		0			0
$673$			24.4099i			0.940934i	0.882418	+	0.470467i	$0.155914\pi$
$673$			24.4099i			0.940934i	−0.882418	+	0.470467i	$0.844086\pi$
$674$	−8.49242	+	2.04496i	−0.327116	+	0.0787689i
$675$		0			0
$676$	9.68466	−	4.95118i	0.372487	−	0.190430i
$677$			40.3803i			1.55194i	0.630770	+	0.775970i	$0.282739\pi$
$677$			40.3803i			1.55194i	−0.630770	+	0.775970i	$0.717261\pi$
$678$		0			0
$679$	−10.0138			−0.384295
$680$	4.71659	+	5.49966i	0.180873	+	0.210902i
$681$		0			0
$682$	4.24621	−	1.02248i	0.162596	−	0.0391528i
$683$	31.5288			1.20642			0.603208	−	0.797584i	$-0.293889\pi$
$683$	31.5288			1.20642			0.603208	+	0.797584i	$0.293889\pi$
$684$		0			0
$685$	31.0540			1.18651
$686$	18.5353	−	4.46326i	0.707680	−	0.170408i
$687$		0			0
$688$	−4.24621	−	3.06744i	−0.161885	−	0.116945i
$689$	42.0540			1.60213
$690$		0			0
$691$			8.01862i			0.305043i	0.988300	+	0.152521i	$0.0487393\pi$
$691$			8.01862i			0.305043i	−0.988300	+	0.152521i	$0.951261\pi$
$692$	−2.19526	−	4.29400i	−0.0834514	−	0.163233i
$693$		0			0
$694$	−41.0664	+	9.88871i	−1.55886	+	0.375370i
$695$			48.5247i			1.84065i
$696$		0			0
$697$		−	5.49966i		−	0.208314i
$698$	−2.99756	−	12.4484i	−0.113459	−	0.471180i
$699$		0			0
$700$	5.90388	+	11.5482i	0.223146	+	0.436480i
$701$	−4.63068			−0.174898			−0.0874492	−	0.996169i	$-0.527872\pi$
$701$	−4.63068			−0.174898			−0.0874492	+	0.996169i	$0.527872\pi$
$702$		0			0
$703$	−12.8255	−	20.2530i	−0.483721	−	0.763858i
$704$	18.4384	+	2.84329i	0.694925	+	0.107160i
$705$		0			0
$706$	6.18606	+	25.6898i	0.232815	+	0.966848i
$707$		−	34.2453i		−	1.28793i
$708$		0			0
$709$	12.6307			0.474355			0.237178	−	0.971466i	$-0.423778\pi$
$709$	12.6307			0.474355			0.237178	+	0.971466i	$0.423778\pi$
$710$	1.75379	+	7.28323i	0.0658185	+	0.273335i
$711$		0			0
$712$	−30.2462	+	25.9396i	−1.13352	+	0.972128i
$713$			2.41131i			0.0903042i
$714$		0			0
$715$	25.6509			0.959290
$716$	−14.4401	+	7.38235i	−0.539651	+	0.275891i
$717$		0			0
$718$	8.52146	−	2.05195i	0.318018	−	0.0765782i
$719$			26.4509i			0.986450i	0.869902	+	0.493225i	$0.164182\pi$
$719$			26.4509i			0.986450i	−0.869902	+	0.493225i	$0.835818\pi$
$720$		0			0
$721$		−	50.1739i		−	1.86858i
$722$	−26.3049	−	5.48200i	−0.978967	−	0.204019i
$723$		0			0
$724$	−17.8324	−	34.8806i	−0.662735	−	1.29633i
$725$		−	1.88269i		−	0.0699215i
$726$		0			0
$727$		−	44.6589i		−	1.65631i	−0.560500	−	0.828154i	$-0.689391\pi$
$727$		−	44.6589i		−	1.65631i	0.560500	−	0.828154i	$-0.310609\pi$
$728$	32.8348	+	38.2861i	1.21694	+	1.41898i
$729$		0			0
$730$	0.104402	+	0.433567i	0.00386410	+	0.0160471i
$731$		−	1.30957i		−	0.0484361i
$732$		0			0
$733$	−5.12311			−0.189226			−0.0946131	−	0.995514i	$-0.530161\pi$
$733$	−5.12311			−0.189226			−0.0946131	+	0.995514i	$0.530161\pi$
$734$	−1.40582	+	0.338519i	−0.0518898	+	0.0124950i
$735$		0			0
$736$	−3.90928	+	9.52935i	−0.144098	+	0.351256i
$737$			0.677039i			0.0249390i
$738$		0			0
$739$		−	25.2042i		−	0.927152i	−0.886057	−	0.463576i	$-0.846566\pi$
$739$		−	25.2042i		−	0.927152i	0.886057	−	0.463576i	$-0.153434\pi$
$740$	12.8255	+	25.0870i	0.471473	+	0.922215i
$741$		0			0
$742$	13.4654	+	55.9200i	0.494332	+	2.05289i
$743$	11.9188			0.437257			0.218628	−	0.975808i	$-0.429842\pi$
$743$	11.9188			0.437257			0.218628	+	0.975808i	$0.429842\pi$
$744$		0			0
$745$	−7.19224			−0.263503
$746$	9.21922	−	2.21997i	0.337540	−	0.0812789i
$747$		0			0
$748$	2.12311	+	4.15286i	0.0776284	+	0.151843i
$749$		−	23.8813i		−	0.872604i
$750$		0			0
$751$	35.6647			1.30142			0.650712	−	0.759324i	$-0.274470\pi$
$751$	35.6647			1.30142			0.650712	+	0.759324i	$0.274470\pi$
$752$	22.6847	+	16.3873i	0.827224	+	0.597582i
$753$		0			0
$754$	−1.71401	−	7.11804i	−0.0624206	−	0.259224i
$755$	−22.6762			−0.825273
$756$		0			0
$757$	−44.8078			−1.62857			−0.814283	−	0.580468i	$-0.802870\pi$
$757$	−44.8078			−1.62857			−0.814283	+	0.580468i	$0.802870\pi$
$758$	−5.21922	−	21.6747i	−0.189571	−	0.787260i
$759$		0			0
$760$	30.1948	+	9.25373i	1.09528	+	0.335668i
$761$	−30.6155			−1.10981			−0.554906	−	0.831913i	$-0.687246\pi$
$761$	−30.6155			−1.10981			−0.554906	+	0.831913i	$0.687246\pi$
$762$		0			0
$763$	50.6855			1.83494
$764$	−7.09612	−	13.8802i	−0.256729	−	0.502168i
$765$		0			0
$766$	−7.36932	−	30.6037i	−0.266264	−	1.10576i
$767$		−	27.1862i		−	0.981638i
$768$		0			0
$769$	−28.2311			−1.01804			−0.509019	−	0.860755i	$-0.669992\pi$
$769$	−28.2311			−1.01804			−0.509019	+	0.860755i	$0.669992\pi$
$770$	8.21327	+	34.1085i	0.295986	+	1.22919i
$771$		0			0
$772$	−5.00691	−	9.79366i	−0.180203	−	0.352481i
$773$		−	41.0573i		−	1.47673i	−0.674402	−	0.738365i	$-0.735598\pi$
$773$		−	41.0573i		−	1.47673i	0.674402	−	0.738365i	$-0.264402\pi$
$774$		0			0
$775$	−2.06798			−0.0742839
$776$	5.17708	−	4.43994i	0.185846	−	0.159385i
$777$		0			0
$778$	4.90251	+	20.3594i	0.175763	+	0.729920i
$779$	−12.8255	−	20.2530i	−0.459520	−	0.725640i
$780$		0			0
$781$			4.82262i			0.172567i
$782$	−2.50345	+	0.602827i	−0.0895233	+	0.0215571i
$783$		0			0
$784$	−24.0000	+	33.2228i	−0.857143	+	1.18653i
$785$	15.3693			0.548554
$786$		0			0
$787$	−26.3588			−0.939591			−0.469796	−	0.882775i	$-0.655672\pi$
$787$	−26.3588			−0.939591			−0.469796	+	0.882775i	$0.655672\pi$
$788$	−40.0540	+	20.4772i	−1.42686	+	0.729470i
$789$		0			0
$790$	11.3693	+	47.2151i	0.404502	+	1.67984i
$791$	22.8393			0.812071
$792$		0			0
$793$			50.1739i			1.78173i
$794$	1.30142	+	5.40461i	0.0461856	+	0.191802i
$795$		0			0
$796$	−4.71165	−	9.21612i	−0.167000	−	0.326657i
$797$		−	23.2043i		−	0.821938i	−0.911649	−	0.410969i	$-0.865191\pi$
$797$		−	23.2043i		−	0.821938i	0.911649	−	0.410969i	$-0.134809\pi$
$798$		0			0
$799$			6.99614i			0.247506i
$800$	−8.17252	−	3.35265i	−0.288942	−	0.118534i
$801$		0			0
$802$	−10.8769	+	2.61914i	−0.384076	+	0.0924849i
$803$			0.287088i			0.0101311i
$804$		0			0
$805$	−19.3693			−0.682679
$806$	−7.81855	+	1.88269i	−0.275397	+	0.0663150i
$807$		0			0
$808$	15.1838	+	17.7046i	0.534163	+	0.622846i
$809$	−44.3693			−1.55994			−0.779971	−	0.625816i	$-0.784766\pi$
$809$	−44.3693			−1.55994			−0.779971	+	0.625816i	$0.784766\pi$
$810$		0			0
$811$	−29.9142			−1.05043			−0.525214	−	0.850970i	$-0.676015\pi$
$811$	−29.9142			−1.05043			−0.525214	+	0.850970i	$0.676015\pi$
$812$	8.91618	−	4.55831i	0.312897	−	0.159965i
$813$		0			0
$814$	4.24621	+	17.6339i	0.148830	+	0.618068i
$815$		−	45.1702i		−	1.58224i
$816$		0			0
$817$	−3.05398	−	4.82262i	−0.106845	−	0.168722i
$818$	−37.8078	+	9.10404i	−1.32192	+	0.318315i
$819$		0			0
$820$	12.8255	+	25.0870i	0.447884	+	0.876075i
$821$	28.4233			0.991980			0.495990	−	0.868328i	$-0.334805\pi$
$821$	28.4233			0.991980			0.495990	+	0.868328i	$0.334805\pi$
$822$		0			0
$823$			31.1150i			1.08460i	0.840185	+	0.542299i	$0.182446\pi$
$823$			31.1150i			1.08460i	−0.840185	+	0.542299i	$0.817554\pi$
$824$	22.2462	+	25.9396i	0.774983	+	0.903649i
$825$		0			0
$826$	36.1501	−	8.70488i	1.25782	−	0.302881i
$827$	49.5242			1.72212			0.861062	−	0.508499i	$-0.169800\pi$
$827$	49.5242			1.72212			0.861062	+	0.508499i	$0.169800\pi$
$828$		0			0
$829$			43.4686i			1.50973i	0.655881	+	0.754864i	$0.272297\pi$
$829$			43.4686i			1.50973i	−0.655881	+	0.754864i	$0.727703\pi$
$830$	42.0775	−	10.1322i	1.46053	−	0.351693i
$831$		0			0
$832$	−33.9507	−	5.23535i	−1.17703	−	0.181503i
$833$	−10.2462			−0.355010
$834$		0			0
$835$	27.5559			0.953610
$836$	17.5032	+	10.3421i	0.605361	+	0.357690i
$837$		0			0
$838$	−54.9029	+	13.2205i	−1.89659	+	0.456695i
$839$	15.8917			0.548642			0.274321	−	0.961638i	$-0.411547\pi$
$839$	15.8917			0.548642			0.274321	+	0.961638i	$0.411547\pi$
$840$		0			0
$841$	27.5464			0.949876
$842$	−31.9039	+	7.68240i	−1.09948	+	0.264753i
$843$		0			0
$844$	44.8712	−	22.9400i	1.54453	−	0.789626i
$845$	−13.9309			−0.479236
$846$		0			0
$847$		−	23.0963i		−	0.793599i
$848$	−31.7555	−	22.9400i	−1.09049	−	0.787762i
$849$		0			0
$850$	−0.516994	−	2.14700i	−0.0177327	−	0.0736415i
$851$	−10.0138			−0.343269
$852$		0			0
$853$	31.3693			1.07406			0.537032	−	0.843562i	$-0.319545\pi$
$853$	31.3693			1.07406			0.537032	+	0.843562i	$0.319545\pi$
$854$	−66.7173	+	16.0654i	−2.28302	+	0.549747i
$855$		0			0
$856$	10.5885	+	12.3465i	0.361909	+	0.421994i
$857$			39.1746i			1.33818i	0.743181	+	0.669090i	$0.233316\pi$
$857$			39.1746i			1.33818i	−0.743181	+	0.669090i	$0.766684\pi$
$858$		0			0
$859$		−	45.9056i		−	1.56628i	−0.621847	−	0.783139i	$-0.713617\pi$
$859$		−	45.9056i		−	1.56628i	0.621847	−	0.783139i	$-0.286383\pi$
$860$	3.05398	+	5.97366i	0.104140	+	0.203700i
$861$		0			0
$862$	−1.75379	−	7.28323i	−0.0597343	−	0.248068i
$863$	−23.4199			−0.797223			−0.398612	−	0.917120i	$-0.630508\pi$
$863$	−23.4199			−0.797223			−0.398612	+	0.917120i	$0.630508\pi$
$864$		0			0
$865$			6.17669i			0.210014i
$866$	−26.0000	+	6.26075i	−0.883516	+	0.212749i
$867$		0			0
$868$	−5.00691	−	9.79366i	−0.169946	−	0.332418i
$869$			31.2637i			1.06055i
$870$		0			0
$871$		−	1.24663i		−	0.0422405i
$872$	−26.2041	+	22.4730i	−0.887382	+	0.761032i
$873$		0			0
$874$	−7.81340	+	8.05815i	−0.264292	+	0.272571i
$875$			36.5774i			1.23654i
$876$		0			0
$877$		−	12.8820i		−	0.434994i	−0.976061	−	0.217497i	$-0.930211\pi$
$877$		−	12.8820i		−	0.434994i	0.976061	−	0.217497i	$-0.0697893\pi$
$878$	−6.49242	−	26.9621i	−0.219109	−	0.909927i
$879$		0			0
$880$	−19.3693	−	13.9923i	−0.652940	−	0.471680i
$881$	10.1771			0.342875			0.171437	−	0.985195i	$-0.445159\pi$
$881$	10.1771			0.342875			0.171437	+	0.985195i	$0.445159\pi$
$882$		0			0
$883$			48.5247i			1.63299i	0.577355	+	0.816493i	$0.304085\pi$
$883$			48.5247i			1.63299i	−0.577355	+	0.816493i	$0.695915\pi$
$884$	−3.90928	−	7.64666i	−0.131483	−	0.257185i
$885$		0			0
$886$	16.8213	−	4.05053i	0.565122	−	0.136080i
$887$	23.0023			0.772342			0.386171	−	0.922427i	$-0.373797\pi$
$887$	23.0023			0.772342			0.386171	+	0.922427i	$0.373797\pi$
$888$		0			0
$889$		−	25.0870i		−	0.841390i
$890$	49.6155	−	11.9473i	1.66312	−	0.400475i
$891$		0			0
$892$	−39.6377	+	20.2644i	−1.32717	+	0.678501i
$893$	16.3153	+	25.7640i	0.545972	+	0.862160i
$894$		0			0
$895$	20.7713			0.694308
$896$	−3.90928	−	46.8213i	−0.130600	−	1.56419i
$897$		0			0
$898$	−20.3002	+	4.88825i	−0.677426	+	0.163123i
$899$			1.59666i			0.0532515i
$900$		0			0
$901$		−	9.79366i		−	0.326274i
$902$	4.24621	+	17.6339i	0.141383	+	0.587145i
$903$		0			0
$904$	−11.8078	+	10.1265i	−0.392720	+	0.336803i
$905$			50.1739i			1.66784i
$906$		0			0
$907$	−25.0345			−0.831258			−0.415629	−	0.909534i	$-0.636439\pi$
$907$	−25.0345			−0.831258			−0.415629	+	0.909534i	$0.636439\pi$
$908$	43.8373	−	22.4114i	1.45479	−	0.743747i
$909$		0			0
$910$	−15.1231	−	62.8041i	−0.501326	−	2.08193i
$911$	−40.3813			−1.33789			−0.668946	−	0.743311i	$-0.733254\pi$
$911$	−40.3813			−1.33789			−0.668946	+	0.743311i	$0.733254\pi$
$912$		0			0
$913$	27.8617			0.922089
$914$	−1.28355	−	5.33040i	−0.0424560	−	0.176314i
$915$		0			0
$916$	11.6847	−	5.97366i	0.386072	−	0.197375i
$917$	−24.8078			−0.819225
$918$		0			0
$919$		−	24.1188i		−	0.795606i	−0.917471	−	0.397803i	$-0.869773\pi$
$919$		−	24.1188i		−	0.795606i	0.917471	−	0.397803i	$-0.130227\pi$
$920$	10.0138	−	8.58800i	0.330146	−	0.283138i
$921$		0			0
$922$	10.4901	+	43.5637i	0.345471	+	1.43469i
$923$		−	8.87989i		−	0.292285i
$924$		0			0
$925$		−	8.58800i		−	0.282372i
$926$	−22.4446	+	5.40461i	−0.737574	+	0.177606i
$927$		0			0
$928$	−2.58854	+	6.30989i	−0.0849730	+	0.207132i
$929$	13.3153			0.436862			0.218431	−	0.975852i	$-0.429906\pi$
$929$	13.3153			0.436862			0.218431	+	0.975852i	$0.429906\pi$
$930$		0			0
$931$	−37.7327	+	23.8947i	−1.23664	+	0.783116i
$932$	19.2462	−	9.83943i	0.630431	−	0.322301i
$933$		0			0
$934$	−3.20636	+	0.772087i	−0.104915	+	0.0252635i
$935$		−	5.97366i		−	0.195360i
$936$		0			0
$937$	−13.8769			−0.453338			−0.226669	−	0.973972i	$-0.572784\pi$
$937$	−13.8769			−0.453338			−0.226669	+	0.973972i	$0.572784\pi$
$938$	1.65767	−	0.399164i	0.0541249	−	0.0130332i
$939$		0			0
$940$	−16.3153	−	31.9133i	−0.532148	−	1.04090i
$941$		−	48.2912i		−	1.57425i	−0.616794	−	0.787125i	$-0.711569\pi$
$941$		−	48.2912i		−	1.57425i	0.616794	−	0.787125i	$-0.288431\pi$
$942$		0			0
$943$	−10.0138			−0.326095
$944$	−14.8298	+	20.5287i	−0.482669	+	0.668151i
$945$		0			0
$946$	1.01110	+	4.19895i	0.0328737	+	0.136520i
$947$		−	21.2755i		−	0.691361i	−0.938352	−	0.345681i	$-0.887648\pi$
$947$		−	21.2755i		−	0.691361i	0.938352	−	0.345681i	$-0.112352\pi$
$948$		0			0
$949$		−	0.528616i		−	0.0171596i
$950$	−6.91079	−	6.70089i	−0.224216	−	0.217406i
$951$		0			0
$952$	8.91618	−	7.64666i	0.288975	−	0.247830i
$953$			31.2637i			1.01273i	0.862319	+	0.506365i	$0.169011\pi$
$953$			31.2637i			1.01273i	−0.862319	+	0.506365i	$0.830989\pi$
$954$		0			0
$955$			19.9660i			0.646083i
$956$	−8.95786	−	17.5218i	−0.289718	−	0.566696i
$957$		0			0
$958$	57.0982	−	13.7491i	1.84476	−	0.444215i
$959$		−	50.3455i		−	1.62574i
$960$		0			0
$961$	−29.2462			−0.943426
$962$	−7.81855	−	32.4693i	−0.252080	−	1.04685i
$963$		0			0
$964$	−20.6440	−	40.3803i	−0.664899	−	1.30056i
$965$			14.0877i			0.453498i
$966$		0			0
$967$			10.3507i			0.332855i	0.986054	+	0.166428i	$0.0532232\pi$
$967$			10.3507i			0.332855i	−0.986054	+	0.166428i	$0.946777\pi$
$968$	10.2405	+	11.9407i	0.329142	+	0.383787i
$969$		0			0
$970$	−8.49242	+	2.04496i	−0.272675	+	0.0656597i
$971$	0.580639			0.0186336			0.00931679	−	0.999957i	$-0.497034\pi$
$971$	0.580639			0.0186336			0.00931679	+	0.999957i	$0.497034\pi$
$972$		0			0
$973$	78.6695			2.52203
$974$	−6.24621	−	25.9396i	−0.200142	−	0.831159i
$975$		0			0
$976$	27.3693	−	37.8869i	0.876070	−	1.21273i
$977$		−	50.8510i		−	1.62687i	−0.581658	−	0.813433i	$-0.697596\pi$
$977$		−	50.8510i		−	1.62687i	0.581658	−	0.813433i	$-0.302404\pi$
$978$		0			0
$979$	32.8531			1.04999
$980$	46.7386	−	23.8947i	1.49301	−	0.763287i
$981$		0			0
$982$	−29.2520	+	7.04383i	−0.933469	+	0.224778i
$983$	6.78456			0.216394			0.108197	−	0.994129i	$-0.465492\pi$
$983$	6.78456			0.216394			0.108197	+	0.994129i	$0.465492\pi$
$984$		0			0
$985$	57.6155			1.83578
$986$	−1.65767	+	0.399164i	−0.0527910	+	0.0127120i
$987$		0			0
$988$	−32.2287	−	19.0430i	−1.02533	−	0.605838i
$989$	−2.38447			−0.0758218
$990$		0			0
$991$	0.417609			0.0132658			0.00663289	−	0.999978i	$-0.497889\pi$
$991$	0.417609			0.0132658			0.00663289	+	0.999978i	$0.497889\pi$
$992$	6.93087	+	2.84329i	0.220055	+	0.0902745i
$993$		0			0
$994$	11.8078	−	2.84329i	0.374520	−	0.0901836i
$995$			13.2569i			0.420272i
$996$		0			0
$997$	41.5464			1.31579			0.657894	−	0.753111i	$-0.271448\pi$
$997$	41.5464			1.31579			0.657894	+	0.753111i	$0.271448\pi$
$998$	−1.80054	+	0.433567i	−0.0569952	+	0.0137243i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.f.b.379.3		8
3.2	odd	2		76.2.d.a.75.6	yes	8
4.3	odd	2	inner	684.2.f.b.379.5		8
12.11	even	2		76.2.d.a.75.4	yes	8
19.18	odd	2	inner	684.2.f.b.379.6		8
24.5	odd	2		1216.2.h.d.1215.1		8
24.11	even	2		1216.2.h.d.1215.8		8
57.56	even	2		76.2.d.a.75.3	✓	8
76.75	even	2	inner	684.2.f.b.379.4		8
228.227	odd	2		76.2.d.a.75.5	yes	8
456.227	odd	2		1216.2.h.d.1215.2		8
456.341	even	2		1216.2.h.d.1215.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.d.a.75.3	✓	8	57.56	even	2
76.2.d.a.75.4	yes	8	12.11	even	2
76.2.d.a.75.5	yes	8	228.227	odd	2
76.2.d.a.75.6	yes	8	3.2	odd	2
684.2.f.b.379.3		8	1.1	even	1	trivial
684.2.f.b.379.4		8	76.75	even	2	inner
684.2.f.b.379.5		8	4.3	odd	2	inner
684.2.f.b.379.6		8	19.18	odd	2	inner
1216.2.h.d.1215.1		8	24.5	odd	2
1216.2.h.d.1215.2		8	456.227	odd	2
1216.2.h.d.1215.7		8	456.341	even	2
1216.2.h.d.1215.8		8	24.11	even	2

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.331077 - 1.37491i) q^{2} +(-1.78078 + 0.910404i) q^{4} +2.56155 q^{5} -4.15286i q^{7} +(1.84130 + 2.14700i) q^{8} +O(q^{10})\)	\(q+(-0.331077 - 1.37491i) q^{2} +(-1.78078 + 0.910404i) q^{4} +2.56155 q^{5} -4.15286i q^{7} +(1.84130 + 2.14700i) q^{8} +(-0.848071 - 3.52191i) q^{10} -2.33205i q^{11} +4.29400i q^{13} +(-5.70982 + 1.37491i) q^{14} +(2.34233 - 3.24245i) q^{16} +1.00000 q^{17} +(3.68260 - 2.33205i) q^{19} +(-4.56155 + 2.33205i) q^{20} +(-3.20636 + 0.772087i) q^{22} -1.82081i q^{23} +1.56155 q^{25} +(5.90388 - 1.42164i) q^{26} +(3.78078 + 7.39531i) q^{28} -1.20565i q^{29} -1.32431 q^{31} +(-5.23358 - 2.14700i) q^{32} +(-0.331077 - 1.37491i) q^{34} -10.6378i q^{35} -5.49966i q^{37} +(-4.42559 - 4.29117i) q^{38} +(4.71659 + 5.49966i) q^{40} -5.49966i q^{41} -1.30957i q^{43} +(2.12311 + 4.15286i) q^{44} +(-2.50345 + 0.602827i) q^{46} +6.99614i q^{47} -10.2462 q^{49} +(-0.516994 - 2.14700i) q^{50} +(-3.90928 - 7.64666i) q^{52} -9.79366i q^{53} -5.97366i q^{55} +(8.91618 - 7.64666i) q^{56} +(-1.65767 + 0.399164i) q^{58} -6.33122 q^{59} +11.6847 q^{61} +(0.438447 + 1.82081i) q^{62} +(-1.21922 + 7.90655i) q^{64} +10.9993i q^{65} -0.290319 q^{67} +(-1.78078 + 0.910404i) q^{68} +(-14.6260 + 3.52191i) q^{70} -2.06798 q^{71} -0.123106 q^{73} +(-7.56155 + 1.82081i) q^{74} +(-4.43478 + 7.50551i) q^{76} -9.68466 q^{77} -13.4061 q^{79} +(6.00000 - 8.30571i) q^{80} +(-7.56155 + 1.82081i) q^{82} +11.9473i q^{83} +2.56155 q^{85} +(-1.80054 + 0.433567i) q^{86} +(5.00691 - 4.29400i) q^{88} +14.0877i q^{89} +17.8324 q^{91} +(1.65767 + 3.24245i) q^{92} +(9.61909 - 2.31626i) q^{94} +(9.43318 - 5.97366i) q^{95} -2.41131i q^{97} +(3.39228 + 14.0877i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{4} + 4 q^{5}+O(q^{10}) \) 8 * q - 6 * q^4 + 4 * q^5	\( 8 q - 6 q^{4} + 4 q^{5} - 6 q^{16} + 8 q^{17} - 20 q^{20} - 4 q^{25} + 6 q^{26} + 22 q^{28} - 18 q^{38} - 16 q^{44} - 16 q^{49} - 38 q^{58} + 44 q^{61} + 20 q^{62} - 18 q^{64} - 6 q^{68} + 32 q^{73} - 44 q^{74} - 16 q^{76} - 28 q^{77} + 48 q^{80} - 44 q^{82} + 4 q^{85} + 38 q^{92}+O(q^{100}) \) 8 * q - 6 * q^4 + 4 * q^5 - 6 * q^16 + 8 * q^17 - 20 * q^20 - 4 * q^25 + 6 * q^26 + 22 * q^28 - 18 * q^38 - 16 * q^44 - 16 * q^49 - 38 * q^58 + 44 * q^61 + 20 * q^62 - 18 * q^64 - 6 * q^68 + 32 * q^73 - 44 * q^74 - 16 * q^76 - 28 * q^77 + 48 * q^80 - 44 * q^82 + 4 * q^85 + 38 * q^92

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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