LMFDB - Embedded newform 1344.2.s.c.239.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(239,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))

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

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

chi := DirichletCharacter("1344.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.s (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 336)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.18
Character	$\chi$	$=$	1344.239
Dual form			1344.2.s.c.911.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.63649 + 0.567369i) q^{3} +(0.132854 + 0.132854i) q^{5} +1.00000 q^{7} +(2.35619 + 1.85698i) q^{9} +O(q^{10})$	\(q+(1.63649 + 0.567369i) q^{3} +(0.132854 + 0.132854i) q^{5} +1.00000 q^{7} +(2.35619 + 1.85698i) q^{9} +(-0.715349 + 0.715349i) q^{11} +(0.206350 + 0.206350i) q^{13} +(0.142036 + 0.292790i) q^{15} +6.91999i q^{17} +(-5.87341 + 5.87341i) q^{19} +(1.63649 + 0.567369i) q^{21} +6.42354i q^{23} -4.96470i q^{25} +(2.80227 + 4.37576i) q^{27} +(5.00314 - 5.00314i) q^{29} -2.52929i q^{31} +(-1.57653 + 0.764794i) q^{33} +(0.132854 + 0.132854i) q^{35} +(6.15279 - 6.15279i) q^{37} +(0.220613 + 0.454766i) q^{39} +5.19068 q^{41} +(-1.36769 - 1.36769i) q^{43} +(0.0663207 + 0.559735i) q^{45} +0.603632 q^{47} +1.00000 q^{49} +(-3.92619 + 11.3245i) q^{51} +(6.19471 + 6.19471i) q^{53} -0.190073 q^{55} +(-12.9442 + 6.27938i) q^{57} +(5.00050 - 5.00050i) q^{59} +(-6.24649 - 6.24649i) q^{61} +(2.35619 + 1.85698i) q^{63} +0.0548287i q^{65} +(-2.55815 + 2.55815i) q^{67} +(-3.64452 + 10.5120i) q^{69} +0.808658i q^{71} +11.5367i q^{73} +(2.81682 - 8.12467i) q^{75} +(-0.715349 + 0.715349i) q^{77} -3.48456i q^{79} +(2.10322 + 8.75080i) q^{81} +(-0.641645 - 0.641645i) q^{83} +(-0.919345 + 0.919345i) q^{85} +(11.0262 - 5.34895i) q^{87} +11.0057 q^{89} +(0.206350 + 0.206350i) q^{91} +(1.43504 - 4.13916i) q^{93} -1.56061 q^{95} -5.56394 q^{97} +(-3.01389 + 0.357104i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} + 40 q^{7}+O(q^{10}) $ 40 * q - 4 * q^3 + 40 * q^7	$ 40 q - 4 q^{3} + 40 q^{7} + 24 q^{13} - 16 q^{19} - 4 q^{21} + 32 q^{27} + 24 q^{33} - 8 q^{37} + 64 q^{39} - 24 q^{43} - 28 q^{45} + 40 q^{49} + 32 q^{51} - 16 q^{55} - 48 q^{61} - 40 q^{67} + 4 q^{69} - 40 q^{75} + 56 q^{81} - 48 q^{85} - 32 q^{87} + 24 q^{91} + 56 q^{93} + 16 q^{97} - 24 q^{99}+O(q^{100}) $ 40 * q - 4 * q^3 + 40 * q^7 + 24 * q^13 - 16 * q^19 - 4 * q^21 + 32 * q^27 + 24 * q^33 - 8 * q^37 + 64 * q^39 - 24 * q^43 - 28 * q^45 + 40 * q^49 + 32 * q^51 - 16 * q^55 - 48 * q^61 - 40 * q^67 + 4 * q^69 - 40 * q^75 + 56 * q^81 - 48 * q^85 - 32 * q^87 + 24 * q^91 + 56 * q^93 + 16 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	1.63649	+	0.567369i	0.944827	+	0.327570i
$3$	1.63649	+	0.567369i	0.944827	+	0.327570i
$4$		0			0
$5$	0.132854	+	0.132854i	0.0594139	+	0.0594139i	0.736189	−	0.676776i	$-0.236623\pi$
$5$	0.132854	+	0.132854i	0.0594139	+	0.0594139i	−0.676776	+	0.736189i	$0.736623\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$		0			0
$9$	2.35619	+	1.85698i	0.785395	+	0.618995i
$10$		0			0
$11$	−0.715349	+	0.715349i	−0.215686	+	0.215686i	−0.806678	−	0.590992i	$-0.798737\pi$
$11$	−0.715349	+	0.715349i	−0.215686	+	0.215686i	0.590992	+	0.806678i	$0.298737\pi$
$12$		0			0
$13$	0.206350	+	0.206350i	0.0572313	+	0.0572313i	0.735143	−	0.677912i	$-0.237115\pi$
$13$	0.206350	+	0.206350i	0.0572313	+	0.0572313i	−0.677912	+	0.735143i	$0.737115\pi$
$14$		0			0
$15$	0.142036	+	0.292790i	0.0366736	+	0.0755981i
$16$		0			0
$17$			6.91999i			1.67834i	0.543866	+	0.839172i	$0.316960\pi$
$17$			6.91999i			1.67834i	−0.543866	+	0.839172i	$0.683040\pi$
$18$		0			0
$19$	−5.87341	+	5.87341i	−1.34745	+	1.34745i	−0.459034	+	0.888419i	$0.651804\pi$
$19$	−5.87341	+	5.87341i	−1.34745	+	1.34745i	−0.888419	+	0.459034i	$0.848196\pi$
$20$		0			0
$21$	1.63649	+	0.567369i	0.357111	+	0.123810i
$22$		0			0
$23$			6.42354i			1.33940i	0.742631	+	0.669701i	$0.233578\pi$
$23$			6.42354i			1.33940i	−0.742631	+	0.669701i	$0.766422\pi$
$24$		0			0
$25$		−	4.96470i		−	0.992940i
$26$		0			0
$27$	2.80227	+	4.37576i	0.539298	+	0.842115i
$28$		0			0
$29$	5.00314	−	5.00314i	0.929059	−	0.929059i	−0.0685860	−	0.997645i	$-0.521849\pi$
$29$	5.00314	−	5.00314i	0.929059	−	0.929059i	0.997645	+	0.0685860i	$0.0218488\pi$
$30$		0			0
$31$		−	2.52929i		−	0.454275i	−0.973863	−	0.227137i	$-0.927063\pi$
$31$		−	2.52929i		−	0.454275i	0.973863	−	0.227137i	$-0.0729366\pi$
$32$		0			0
$33$	−1.57653	+	0.764794i	−0.274438	+	0.133133i
$34$		0			0
$35$	0.132854	+	0.132854i	0.0224563	+	0.0224563i
$36$		0			0
$37$	6.15279	−	6.15279i	1.01151	−	1.01151i	0.0115789	−	0.999933i	$-0.496314\pi$
$37$	6.15279	−	6.15279i	1.01151	−	1.01151i	0.999933	−	0.0115789i	$-0.00368575\pi$
$38$		0			0
$39$	0.220613	+	0.454766i	0.0353264	+	0.0728209i
$40$		0			0
$41$	5.19068			0.810647			0.405324	−	0.914173i	$-0.367159\pi$
$41$	5.19068			0.810647			0.405324	+	0.914173i	$0.367159\pi$
$42$		0			0
$43$	−1.36769	−	1.36769i	−0.208571	−	0.208571i	0.595089	−	0.803660i	$-0.297117\pi$
$43$	−1.36769	−	1.36769i	−0.208571	−	0.208571i	−0.803660	+	0.595089i	$0.797117\pi$
$44$		0			0
$45$	0.0663207	+	0.559735i	0.00988651	+	0.0834403i
$46$		0			0
$47$	0.603632			0.0880487			0.0440244	−	0.999030i	$-0.485982\pi$
$47$	0.603632			0.0880487			0.0440244	+	0.999030i	$0.485982\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$		0			0
$51$	−3.92619	+	11.3245i	−0.549776	+	1.58574i
$52$		0			0
$53$	6.19471	+	6.19471i	0.850909	+	0.850909i	0.990245	−	0.139336i	$-0.0444969\pi$
$53$	6.19471	+	6.19471i	0.850909	+	0.850909i	−0.139336	+	0.990245i	$0.544497\pi$
$54$		0			0
$55$	−0.190073			−0.0256295
$56$		0			0
$57$	−12.9442	+	6.27938i	−1.71449	+	0.831724i
$58$		0			0
$59$	5.00050	−	5.00050i	0.651010	−	0.651010i	−0.302226	−	0.953236i	$-0.597730\pi$
$59$	5.00050	−	5.00050i	0.651010	−	0.651010i	0.953236	+	0.302226i	$0.0977298\pi$
$60$		0			0
$61$	−6.24649	−	6.24649i	−0.799781	−	0.799781i	0.183280	−	0.983061i	$-0.441329\pi$
$61$	−6.24649	−	6.24649i	−0.799781	−	0.799781i	−0.983061	+	0.183280i	$0.941329\pi$
$62$		0			0
$63$	2.35619	+	1.85698i	0.296851	+	0.233958i
$64$		0			0
$65$			0.0548287i			0.00680067i
$66$		0			0
$67$	−2.55815	+	2.55815i	−0.312527	+	0.312527i	−0.845888	−	0.533361i	$-0.820929\pi$
$67$	−2.55815	+	2.55815i	−0.312527	+	0.312527i	0.533361	+	0.845888i	$0.320929\pi$
$68$		0			0
$69$	−3.64452	+	10.5120i	−0.438748	+	1.26550i
$70$		0			0
$71$			0.808658i			0.0959700i	0.998848	+	0.0479850i	$0.0152800\pi$
$71$			0.808658i			0.0959700i	−0.998848	+	0.0479850i	$0.984720\pi$
$72$		0			0
$73$			11.5367i			1.35027i	0.737695	+	0.675134i	$0.235914\pi$
$73$			11.5367i			1.35027i	−0.737695	+	0.675134i	$0.764086\pi$
$74$		0			0
$75$	2.81682	−	8.12467i	0.325258	−	0.938156i
$76$		0			0
$77$	−0.715349	+	0.715349i	−0.0815216	+	0.0815216i
$78$		0			0
$79$		−	3.48456i		−	0.392044i	−0.980600	−	0.196022i	$-0.937198\pi$
$79$		−	3.48456i		−	0.392044i	0.980600	−	0.196022i	$-0.0628024\pi$
$80$		0			0
$81$	2.10322	+	8.75080i	0.233691	+	0.972311i
$82$		0			0
$83$	−0.641645	−	0.641645i	−0.0704297	−	0.0704297i	0.671015	−	0.741444i	$-0.265859\pi$
$83$	−0.641645	−	0.641645i	−0.0704297	−	0.0704297i	−0.741444	+	0.671015i	$0.765859\pi$
$84$		0			0
$85$	−0.919345	+	0.919345i	−0.0997170	+	0.0997170i
$86$		0			0
$87$	11.0262	−	5.34895i	1.18213	−	0.573468i
$88$		0			0
$89$	11.0057			1.16661			0.583303	−	0.812254i	$-0.301760\pi$
$89$	11.0057			1.16661			0.583303	+	0.812254i	$0.301760\pi$
$90$		0			0
$91$	0.206350	+	0.206350i	0.0216314	+	0.0216314i
$92$		0			0
$93$	1.43504	−	4.13916i	0.148807	−	0.429211i
$94$		0			0
$95$	−1.56061			−0.160115
$96$		0			0
$97$	−5.56394			−0.564933			−0.282466	−	0.959277i	$-0.591153\pi$
$97$	−5.56394			−0.564933			−0.282466	+	0.959277i	$0.591153\pi$
$98$		0			0
$99$	−3.01389	+	0.357104i	−0.302907	+	0.0358903i
$100$		0			0
$101$	−7.49292	−	7.49292i	−0.745574	−	0.745574i	0.228071	−	0.973645i	$-0.426758\pi$
$101$	−7.49292	−	7.49292i	−0.745574	−	0.745574i	−0.973645	+	0.228071i	$0.926758\pi$
$102$		0			0
$103$	0.568966			0.0560619			0.0280309	−	0.999607i	$-0.491076\pi$
$103$	0.568966			0.0560619			0.0280309	+	0.999607i	$0.491076\pi$
$104$		0			0
$105$	0.142036	+	0.292790i	0.0138613	+	0.0285734i
$106$		0			0
$107$	−5.79066	+	5.79066i	−0.559804	+	0.559804i	−0.929252	−	0.369447i	$-0.879547\pi$
$107$	−5.79066	+	5.79066i	−0.559804	+	0.559804i	0.369447	+	0.929252i	$0.379547\pi$
$108$		0			0
$109$	−5.70587	−	5.70587i	−0.546523	−	0.546523i	0.378910	−	0.925433i	$-0.376299\pi$
$109$	−5.70587	−	5.70587i	−0.546523	−	0.546523i	−0.925433	+	0.378910i	$0.876299\pi$
$110$		0			0
$111$	13.5599	−	6.57806i	1.28704	−	0.624362i
$112$		0			0
$113$		−	5.81929i		−	0.547433i	−0.961810	−	0.273716i	$-0.911747\pi$
$113$		−	5.81929i		−	0.547433i	0.961810	−	0.273716i	$-0.0882530\pi$
$114$		0			0
$115$	−0.853390	+	0.853390i	−0.0795791	+	0.0795791i
$116$		0			0
$117$	0.103010	+	0.869389i	0.00952332	+	0.0803750i
$118$		0			0
$119$			6.91999i			0.634354i
$120$		0			0
$121$			9.97655i			0.906959i
$122$		0			0
$123$	8.49448	+	2.94503i	0.765921	+	0.265544i
$124$		0			0
$125$	1.32385	−	1.32385i	0.118408	−	0.118408i
$126$		0			0
$127$		−	15.2053i		−	1.34925i	−0.738160	−	0.674626i	$-0.764305\pi$
$127$		−	15.2053i		−	1.34925i	0.738160	−	0.674626i	$-0.235695\pi$
$128$		0			0
$129$	−1.46223	−	3.01420i	−0.128742	−	0.265386i
$130$		0			0
$131$	−7.26058	−	7.26058i	−0.634359	−	0.634359i	0.314799	−	0.949158i	$-0.398063\pi$
$131$	−7.26058	−	7.26058i	−0.634359	−	0.634359i	−0.949158	+	0.314799i	$0.898063\pi$
$132$		0			0
$133$	−5.87341	+	5.87341i	−0.509289	+	0.509289i
$134$		0			0
$135$	−0.209043	+	0.953627i	−0.0179915	+	0.0820752i
$136$		0			0
$137$	−3.38132			−0.288886			−0.144443	−	0.989513i	$-0.546139\pi$
$137$	−3.38132			−0.288886			−0.144443	+	0.989513i	$0.546139\pi$
$138$		0			0
$139$	−6.15797	−	6.15797i	−0.522312	−	0.522312i	0.395957	−	0.918269i	$-0.370413\pi$
$139$	−6.15797	−	6.15797i	−0.522312	−	0.522312i	−0.918269	+	0.395957i	$0.870413\pi$
$140$		0			0
$141$	0.987836	+	0.342482i	0.0831908	+	0.0288422i
$142$		0			0
$143$	−0.295225			−0.0246880
$144$		0			0
$145$	1.32937			0.110398
$146$		0			0
$147$	1.63649	+	0.567369i	0.134975	+	0.0467958i
$148$		0			0
$149$	3.57067	+	3.57067i	0.292520	+	0.292520i	0.838075	−	0.545555i	$-0.183681\pi$
$149$	3.57067	+	3.57067i	0.292520	+	0.292520i	−0.545555	+	0.838075i	$0.683681\pi$
$150$		0			0
$151$	2.30493			0.187573			0.0937864	−	0.995592i	$-0.470103\pi$
$151$	2.30493			0.187573			0.0937864	+	0.995592i	$0.470103\pi$
$152$		0			0
$153$	−12.8503	+	16.3048i	−1.03889	+	1.31816i
$154$		0			0
$155$	0.336026	−	0.336026i	0.0269902	−	0.0269902i
$156$		0			0
$157$	−12.0921	−	12.0921i	−0.965054	−	0.965054i	0.0343560	−	0.999410i	$-0.489062\pi$
$157$	−12.0921	−	12.0921i	−0.965054	−	0.965054i	−0.999410	+	0.0343560i	$0.989062\pi$
$158$		0			0
$159$	6.62288	+	13.6523i	0.525229	+	1.08269i
$160$		0			0
$161$			6.42354i			0.506246i
$162$		0			0
$163$	1.08738	−	1.08738i	0.0851704	−	0.0851704i	−0.663238	−	0.748408i	$-0.730818\pi$
$163$	1.08738	−	1.08738i	0.0851704	−	0.0851704i	0.748408	+	0.663238i	$0.230818\pi$
$164$		0			0
$165$	−0.311053	−	0.107842i	−0.0242154	−	0.00839546i
$166$		0			0
$167$			20.3703i			1.57630i	0.615484	+	0.788149i	$0.288961\pi$
$167$			20.3703i			1.57630i	−0.615484	+	0.788149i	$0.711039\pi$
$168$		0			0
$169$		−	12.9148i		−	0.993449i
$170$		0			0
$171$	−24.7457	+	2.93202i	−1.89235	+	0.224217i
$172$		0			0
$173$	2.77906	−	2.77906i	0.211288	−	0.211288i	−0.593527	−	0.804814i	$-0.702265\pi$
$173$	2.77906	−	2.77906i	0.211288	−	0.211288i	0.804814	+	0.593527i	$0.202265\pi$
$174$		0			0
$175$		−	4.96470i		−	0.375296i
$176$		0			0
$177$	11.0204	−	5.34613i	0.828343	−	0.401840i
$178$		0			0
$179$	−8.23312	−	8.23312i	−0.615372	−	0.615372i	0.328969	−	0.944341i	$-0.393299\pi$
$179$	−8.23312	−	8.23312i	−0.615372	−	0.615372i	−0.944341	+	0.328969i	$0.893299\pi$
$180$		0			0
$181$	4.91780	−	4.91780i	0.365537	−	0.365537i	−0.500310	−	0.865847i	$-0.666780\pi$
$181$	4.91780	−	4.91780i	0.365537	−	0.365537i	0.865847	+	0.500310i	$0.166780\pi$
$182$		0			0
$183$	−6.67824	−	13.7664i	−0.493670	−	1.01764i
$184$		0			0
$185$	1.63484			0.120196
$186$		0			0
$187$	−4.95021	−	4.95021i	−0.361995	−	0.361995i
$188$		0			0
$189$	2.80227	+	4.37576i	0.203836	+	0.318290i
$190$		0			0
$191$	18.9768			1.37312			0.686558	−	0.727075i	$-0.259121\pi$
$191$	18.9768			1.37312			0.686558	+	0.727075i	$0.259121\pi$
$192$		0			0
$193$	25.6525			1.84651			0.923254	−	0.384191i	$-0.125519\pi$
$193$	25.6525			1.84651			0.923254	+	0.384191i	$0.125519\pi$
$194$		0			0
$195$	−0.0311081	+	0.0897266i	−0.00222770	+	0.00642545i
$196$		0			0
$197$	−16.3956	−	16.3956i	−1.16814	−	1.16814i	−0.982645	−	0.185494i	$-0.940611\pi$
$197$	−16.3956	−	16.3956i	−1.16814	−	1.16814i	−0.185494	−	0.982645i	$-0.559389\pi$
$198$		0			0
$199$	25.9930			1.84260			0.921298	−	0.388857i	$-0.127130\pi$
$199$	25.9930			1.84260			0.921298	+	0.388857i	$0.127130\pi$
$200$		0			0
$201$	−5.63779	+	2.73496i	−0.397659	+	0.192909i
$202$		0			0
$203$	5.00314	−	5.00314i	0.351151	−	0.351151i
$204$		0			0
$205$	0.689600	+	0.689600i	0.0481637	+	0.0481637i
$206$		0			0
$207$	−11.9284	+	15.1351i	−0.829082	+	1.05196i
$208$		0			0
$209$		−	8.40308i		−	0.581253i
$210$		0			0
$211$	13.6935	−	13.6935i	0.942699	−	0.942699i	−0.0557463	−	0.998445i	$-0.517754\pi$
$211$	13.6935	−	13.6935i	0.942699	−	0.942699i	0.998445	+	0.0557463i	$0.0177538\pi$
$212$		0			0
$213$	−0.458807	+	1.32336i	−0.0314369	+	0.0906750i
$214$		0			0
$215$		−	0.363406i		−	0.0247841i
$216$		0			0
$217$		−	2.52929i		−	0.171700i
$218$		0			0
$219$	−6.54556	+	18.8797i	−0.442308	+	1.27577i
$220$		0			0
$221$	−1.42794	+	1.42794i	−0.0960537	+	0.0960537i
$222$		0			0
$223$		−	11.6521i		−	0.780280i	−0.920756	−	0.390140i	$-0.872427\pi$
$223$		−	11.6521i		−	0.780280i	0.920756	−	0.390140i	$-0.127573\pi$
$224$		0			0
$225$	9.21937	−	11.6978i	0.614625	−	0.779850i
$226$		0			0
$227$	−0.211018	−	0.211018i	−0.0140058	−	0.0140058i	0.700069	−	0.714075i	$-0.253152\pi$
$227$	−0.211018	−	0.211018i	−0.0140058	−	0.0140058i	−0.714075	+	0.700069i	$0.753152\pi$
$228$		0			0
$229$	−11.7698	+	11.7698i	−0.777772	+	0.777772i	−0.979452	−	0.201680i	$-0.935360\pi$
$229$	−11.7698	+	11.7698i	−0.777772	+	0.777772i	0.201680	+	0.979452i	$0.435360\pi$
$230$		0			0
$231$	−1.57653	+	0.764794i	−0.103728	+	0.0503197i
$232$		0			0
$233$	6.24518			0.409135			0.204568	−	0.978852i	$-0.434421\pi$
$233$	6.24518			0.409135			0.204568	+	0.978852i	$0.434421\pi$
$234$		0			0
$235$	0.0801946	+	0.0801946i	0.00523132	+	0.00523132i
$236$		0			0
$237$	1.97703	−	5.70245i	0.128422	−	0.370414i
$238$		0			0
$239$	−25.8455			−1.67180			−0.835902	−	0.548878i	$-0.815055\pi$
$239$	−25.8455			−1.67180			−0.835902	+	0.548878i	$0.815055\pi$
$240$		0			0
$241$	18.9857			1.22298			0.611488	−	0.791254i	$-0.290571\pi$
$241$	18.9857			1.22298			0.611488	+	0.791254i	$0.290571\pi$
$242$		0			0
$243$	−1.52303	+	15.5139i	−0.0977025	+	0.995216i
$244$		0			0
$245$	0.132854	+	0.132854i	0.00848770	+	0.00848770i
$246$		0			0
$247$	−2.42396			−0.154233
$248$		0			0
$249$	−0.685995	−	1.41409i	−0.0434732	−	0.0896145i
$250$		0			0
$251$	10.5737	−	10.5737i	0.667407	−	0.667407i	−0.289708	−	0.957115i	$-0.593558\pi$
$251$	10.5737	−	10.5737i	0.667407	−	0.667407i	0.957115	+	0.289708i	$0.0935582\pi$
$252$		0			0
$253$	−4.59508	−	4.59508i	−0.288890	−	0.288890i
$254$		0			0
$255$	−2.02611	+	0.982890i	−0.126880	+	0.0615509i
$256$		0			0
$257$			4.31950i			0.269443i	0.990884	+	0.134722i	$0.0430140\pi$
$257$			4.31950i			0.269443i	−0.990884	+	0.134722i	$0.956986\pi$
$258$		0			0
$259$	6.15279	−	6.15279i	0.382316	−	0.382316i
$260$		0			0
$261$	21.0791	−	2.49757i	1.30476	−	0.154596i
$262$		0			0
$263$			11.9657i			0.737837i	0.929462	+	0.368918i	$0.120272\pi$
$263$			11.9657i			0.737837i	−0.929462	+	0.368918i	$0.879728\pi$
$264$		0			0
$265$			1.64598i			0.101112i
$266$		0			0
$267$	18.0108	+	6.24431i	1.10224	+	0.382146i
$268$		0			0
$269$	−19.4957	+	19.4957i	−1.18867	+	1.18867i	−0.211236	+	0.977435i	$0.567749\pi$
$269$	−19.4957	+	19.4957i	−1.18867	+	1.18867i	−0.977435	+	0.211236i	$0.932251\pi$
$270$		0			0
$271$			4.80008i			0.291584i	0.989315	+	0.145792i	$0.0465730\pi$
$271$			4.80008i			0.291584i	−0.989315	+	0.145792i	$0.953427\pi$
$272$		0			0
$273$	0.220613	+	0.454766i	0.0133521	+	0.0275237i
$274$		0			0
$275$	3.55149	+	3.55149i	0.214163	+	0.214163i
$276$		0			0
$277$	16.1975	−	16.1975i	0.973214	−	0.973214i	−0.0264369	−	0.999650i	$-0.508416\pi$
$277$	16.1975	−	16.1975i	0.973214	−	0.973214i	0.999650	+	0.0264369i	$0.00841612\pi$
$278$		0			0
$279$	4.69686	−	5.95949i	0.281194	−	0.356785i
$280$		0			0
$281$	−16.3201			−0.973575			−0.486787	−	0.873520i	$-0.661831\pi$
$281$	−16.3201			−0.973575			−0.486787	+	0.873520i	$0.661831\pi$
$282$		0			0
$283$	−16.3557	−	16.3557i	−0.972244	−	0.972244i	0.0273808	−	0.999625i	$-0.491283\pi$
$283$	−16.3557	−	16.3557i	−0.972244	−	0.972244i	−0.999625	+	0.0273808i	$0.991283\pi$
$284$		0			0
$285$	−2.55391	−	0.885439i	−0.151281	−	0.0524489i
$286$		0			0
$287$	5.19068			0.306396
$288$		0			0
$289$	−30.8863			−1.81684
$290$		0			0
$291$	−9.10533	−	3.15681i	−0.533764	−	0.185055i
$292$		0			0
$293$	4.80343	+	4.80343i	0.280620	+	0.280620i	0.833356	−	0.552736i	$-0.186416\pi$
$293$	4.80343	+	4.80343i	0.280620	+	0.280620i	−0.552736	+	0.833356i	$0.686416\pi$
$294$		0			0
$295$	1.32867			0.0773581
$296$		0			0
$297$	−5.13480	−	1.12559i	−0.297951	−	0.0653133i
$298$		0			0
$299$	−1.32550	+	1.32550i	−0.0766556	+	0.0766556i
$300$		0			0
$301$	−1.36769	−	1.36769i	−0.0788326	−	0.0788326i
$302$		0			0
$303$	−8.01083	−	16.5133i	−0.460210	−	0.948666i
$304$		0			0
$305$		−	1.65974i		−	0.0950362i
$306$		0			0
$307$	−2.57337	+	2.57337i	−0.146870	+	0.146870i	−0.776718	−	0.629848i	$-0.783117\pi$
$307$	−2.57337	+	2.57337i	−0.146870	+	0.146870i	0.629848	+	0.776718i	$0.283117\pi$
$308$		0			0
$309$	0.931105	+	0.322813i	0.0529687	+	0.0183642i
$310$		0			0
$311$		−	16.8194i		−	0.953741i	−0.878973	−	0.476871i	$-0.841771\pi$
$311$		−	16.8194i		−	0.953741i	0.878973	−	0.476871i	$-0.158229\pi$
$312$		0			0
$313$		−	3.09458i		−	0.174916i	−0.996168	−	0.0874581i	$-0.972126\pi$
$313$		−	3.09458i		−	0.174916i	0.996168	−	0.0874581i	$-0.0278744\pi$
$314$		0			0
$315$	0.0663207	+	0.559735i	0.00373675	+	0.0315375i
$316$		0			0
$317$	−11.7725	+	11.7725i	−0.661211	+	0.661211i	−0.955665	−	0.294455i	$-0.904862\pi$
$317$	−11.7725	+	11.7725i	−0.661211	+	0.661211i	0.294455	+	0.955665i	$0.404862\pi$
$318$		0			0
$319$			7.15798i			0.400770i
$320$		0			0
$321$	−12.7618	+	6.19091i	−0.712293	+	0.345543i
$322$		0			0
$323$	−40.6439	−	40.6439i	−2.26149	−	2.26149i
$324$		0			0
$325$	1.02447	−	1.02447i	0.0568272	−	0.0568272i
$326$		0			0
$327$	−6.10025	−	12.5749i	−0.337345	−	0.695394i
$328$		0			0
$329$	0.603632			0.0332793
$330$		0			0
$331$	14.8912	+	14.8912i	0.818493	+	0.818493i	0.985890	−	0.167397i	$-0.0535361\pi$
$331$	14.8912	+	14.8912i	0.818493	+	0.818493i	−0.167397	+	0.985890i	$0.553536\pi$
$332$		0			0
$333$	25.9227	−	3.07148i	1.42056	−	0.168316i
$334$		0			0
$335$	−0.679718			−0.0371369
$336$		0			0
$337$	−18.3243			−0.998187			−0.499093	−	0.866548i	$-0.666334\pi$
$337$	−18.3243			−0.998187			−0.499093	+	0.866548i	$0.666334\pi$
$338$		0			0
$339$	3.30168	−	9.52320i	0.179323	−	0.517229i
$340$		0			0
$341$	1.80933	+	1.80933i	0.0979806	+	0.0979806i
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	−1.88075	+	0.912376i	−0.101256	+	0.0491207i
$346$		0			0
$347$	14.0124	−	14.0124i	0.752224	−	0.752224i	−0.222670	−	0.974894i	$-0.571477\pi$
$347$	14.0124	−	14.0124i	0.752224	−	0.752224i	0.974894	+	0.222670i	$0.0714773\pi$
$348$		0			0
$349$	5.78830	+	5.78830i	0.309841	+	0.309841i	0.844848	−	0.535007i	$-0.179691\pi$
$349$	5.78830	+	5.78830i	0.309841	+	0.309841i	−0.535007	+	0.844848i	$0.679691\pi$
$350$		0			0
$351$	−0.324689	+	1.48119i	−0.0173306	+	0.0790600i
$352$		0			0
$353$		−	13.9096i		−	0.740334i	−0.928965	−	0.370167i	$-0.879300\pi$
$353$		−	13.9096i		−	0.740334i	0.928965	−	0.370167i	$-0.120700\pi$
$354$		0			0
$355$	−0.107433	+	0.107433i	−0.00570195	+	0.00570195i
$356$		0			0
$357$	−3.92619	+	11.3245i	−0.207796	+	0.599355i
$358$		0			0
$359$		−	20.7206i		−	1.09359i	−0.837266	−	0.546796i	$-0.815847\pi$
$359$		−	20.7206i		−	1.09359i	0.837266	−	0.546796i	$-0.184153\pi$
$360$		0			0
$361$		−	49.9939i		−	2.63126i
$362$		0			0
$363$	−5.66038	+	16.3265i	−0.297093	+	0.856919i
$364$		0			0
$365$	−1.53269	+	1.53269i	−0.0802247	+	0.0802247i
$366$		0			0
$367$			14.8824i			0.776856i	0.921479	+	0.388428i	$0.126982\pi$
$367$			14.8824i			0.776856i	−0.921479	+	0.388428i	$0.873018\pi$
$368$		0			0
$369$	12.2302	+	9.63900i	0.636679	+	0.501786i
$370$		0			0
$371$	6.19471	+	6.19471i	0.321613	+	0.321613i
$372$		0			0
$373$	10.6598	−	10.6598i	0.551942	−	0.551942i	−0.375059	−	0.927001i	$-0.622377\pi$
$373$	10.6598	−	10.6598i	0.551942	−	0.551942i	0.927001	+	0.375059i	$0.122377\pi$
$374$		0			0
$375$	2.91757	−	1.41535i	0.150662	−	0.0730883i
$376$		0			0
$377$	2.06480			0.106342
$378$		0			0
$379$	5.54417	+	5.54417i	0.284785	+	0.284785i	0.835014	−	0.550229i	$-0.185460\pi$
$379$	5.54417	+	5.54417i	0.284785	+	0.284785i	−0.550229	+	0.835014i	$0.685460\pi$
$380$		0			0
$381$	8.62701	−	24.8833i	0.441975	−	1.27481i
$382$		0			0
$383$	−10.0142			−0.511702			−0.255851	−	0.966716i	$-0.582356\pi$
$383$	−10.0142			−0.511702			−0.255851	+	0.966716i	$0.582356\pi$
$384$		0			0
$385$	−0.190073			−0.00968704
$386$		0			0
$387$	−0.682756	−	5.76233i	−0.0347064	−	0.292916i
$388$		0			0
$389$	−18.2249	−	18.2249i	−0.924041	−	0.924041i	0.0732708	−	0.997312i	$-0.476656\pi$
$389$	−18.2249	−	18.2249i	−0.924041	−	0.924041i	−0.997312	+	0.0732708i	$0.976656\pi$
$390$		0			0
$391$	−44.4508			−2.24798
$392$		0			0
$393$	−7.76242	−	16.0013i	−0.391562	−	0.807157i
$394$		0			0
$395$	0.462937	−	0.462937i	0.0232929	−	0.0232929i
$396$		0			0
$397$	3.09916	+	3.09916i	0.155542	+	0.155542i	0.780588	−	0.625046i	$-0.214920\pi$
$397$	3.09916	+	3.09916i	0.155542	+	0.155542i	−0.625046	+	0.780588i	$0.714920\pi$
$398$		0			0
$399$	−12.9442	+	6.27938i	−0.648018	+	0.314362i
$400$		0			0
$401$			19.8682i			0.992169i	0.868274	+	0.496084i	$0.165229\pi$
$401$			19.8682i			0.992169i	−0.868274	+	0.496084i	$0.834771\pi$
$402$		0			0
$403$	0.521920	−	0.521920i	0.0259987	−	0.0259987i
$404$		0			0
$405$	−0.883154	+	1.44200i	−0.0438843	+	0.0716533i
$406$		0			0
$407$			8.80278i			0.436338i
$408$		0			0
$409$		−	4.49996i		−	0.222509i	−0.993792	−	0.111254i	$-0.964513\pi$
$409$		−	4.49996i		−	0.222509i	0.993792	−	0.111254i	$-0.0354868\pi$
$410$		0			0
$411$	−5.53349	−	1.91845i	−0.272947	−	0.0946304i
$412$		0			0
$413$	5.00050	−	5.00050i	0.246059	−	0.246059i
$414$		0			0
$415$		−	0.170490i		−	0.00836900i
$416$		0			0
$417$	−6.58360	−	13.5713i	−0.322400	−	0.664588i
$418$		0			0
$419$	21.9984	+	21.9984i	1.07469	+	1.07469i	0.996976	+	0.0777158i	$0.0247627\pi$
$419$	21.9984	+	21.9984i	1.07469	+	1.07469i	0.0777158	+	0.996976i	$0.475237\pi$
$420$		0			0
$421$	10.9884	−	10.9884i	0.535542	−	0.535542i	−0.386674	−	0.922216i	$-0.626376\pi$
$421$	10.9884	−	10.9884i	0.535542	−	0.535542i	0.922216	+	0.386674i	$0.126376\pi$
$422$		0			0
$423$	1.42227	+	1.12093i	0.0691530	+	0.0545017i
$424$		0			0
$425$	34.3557			1.66649
$426$		0			0
$427$	−6.24649	−	6.24649i	−0.302289	−	0.302289i
$428$		0			0
$429$	−0.483132	−	0.167501i	−0.0233258	−	0.00808704i
$430$		0			0
$431$	−14.4548			−0.696262			−0.348131	−	0.937446i	$-0.613184\pi$
$431$	−14.4548			−0.696262			−0.348131	+	0.937446i	$0.613184\pi$
$432$		0			0
$433$	6.38419			0.306805			0.153402	−	0.988164i	$-0.450977\pi$
$433$	6.38419			0.306805			0.153402	+	0.988164i	$0.450977\pi$
$434$		0			0
$435$	2.17550	+	0.754242i	0.104307	+	0.0361632i
$436$		0			0
$437$	−37.7281	−	37.7281i	−1.80478	−	1.80478i
$438$		0			0
$439$	21.1960			1.01163			0.505816	−	0.862642i	$-0.331192\pi$
$439$	21.1960			1.01163			0.505816	+	0.862642i	$0.331192\pi$
$440$		0			0
$441$	2.35619	+	1.85698i	0.112199	+	0.0884278i
$442$		0			0
$443$	13.9575	−	13.9575i	0.663141	−	0.663141i	−0.292978	−	0.956119i	$-0.594646\pi$
$443$	13.9575	−	13.9575i	0.663141	−	0.663141i	0.956119	+	0.292978i	$0.0946463\pi$
$444$		0			0
$445$	1.46215	+	1.46215i	0.0693127	+	0.0693127i
$446$		0			0
$447$	3.81747	+	7.86924i	0.180560	+	0.372202i
$448$		0			0
$449$		−	14.1807i		−	0.669228i	−0.942355	−	0.334614i	$-0.891394\pi$
$449$		−	14.1807i		−	0.669228i	0.942355	−	0.334614i	$-0.108606\pi$
$450$		0			0
$451$	−3.71315	+	3.71315i	−0.174845	+	0.174845i
$452$		0			0
$453$	3.77200	+	1.30775i	0.177224	+	0.0614433i
$454$		0			0
$455$			0.0548287i			0.00257041i
$456$		0			0
$457$			37.3522i			1.74726i	0.486590	+	0.873630i	$0.338241\pi$
$457$			37.3522i			1.74726i	−0.486590	+	0.873630i	$0.661759\pi$
$458$		0			0
$459$	−30.2802	+	19.3917i	−1.41336	+	0.905128i
$460$		0			0
$461$	−10.5304	+	10.5304i	−0.490449	+	0.490449i	−0.908448	−	0.417999i	$-0.862732\pi$
$461$	−10.5304	+	10.5304i	−0.490449	+	0.490449i	0.417999	+	0.908448i	$0.362732\pi$
$462$		0			0
$463$		−	26.2737i		−	1.22104i	−0.792000	−	0.610521i	$-0.790960\pi$
$463$		−	26.2737i		−	1.22104i	0.792000	−	0.610521i	$-0.209040\pi$
$464$		0			0
$465$	0.740552	−	0.359252i	0.0343423	−	0.0166599i
$466$		0			0
$467$	20.6885	+	20.6885i	0.957349	+	0.957349i	0.999127	−	0.0417774i	$-0.0133020\pi$
$467$	20.6885	+	20.6885i	0.957349	+	0.957349i	−0.0417774	+	0.999127i	$0.513302\pi$
$468$		0			0
$469$	−2.55815	+	2.55815i	−0.118124	+	0.118124i
$470$		0			0
$471$	−12.9279	−	26.6492i	−0.595685	−	1.22793i
$472$		0			0
$473$	1.95676			0.0899719
$474$		0			0
$475$	29.1597	+	29.1597i	1.33794	+	1.33794i
$476$		0			0
$477$	3.09241	+	26.0994i	0.141592	+	1.19501i
$478$		0			0
$479$	−18.5260			−0.846476			−0.423238	−	0.906018i	$-0.639107\pi$
$479$	−18.5260			−0.846476			−0.423238	+	0.906018i	$0.639107\pi$
$480$		0			0
$481$	2.53926			0.115780
$482$		0			0
$483$	−3.64452	+	10.5120i	−0.165831	+	0.478315i
$484$		0			0
$485$	−0.739190	−	0.739190i	−0.0335649	−	0.0335649i
$486$		0			0
$487$	−36.6140			−1.65914			−0.829570	−	0.558403i	$-0.811414\pi$
$487$	−36.6140			−1.65914			−0.829570	+	0.558403i	$0.811414\pi$
$488$		0			0
$489$	2.39644	−	1.16254i	0.108371	−	0.0525720i
$490$		0			0
$491$	−2.64760	+	2.64760i	−0.119485	+	0.119485i	−0.764321	−	0.644836i	$-0.776926\pi$
$491$	−2.64760	+	2.64760i	−0.119485	+	0.119485i	0.644836	+	0.764321i	$0.276926\pi$
$492$		0			0
$493$	34.6217	+	34.6217i	1.55928	+	1.55928i
$494$		0			0
$495$	−0.447848	−	0.352963i	−0.0201293	−	0.0158645i
$496$		0			0
$497$			0.808658i			0.0362733i
$498$		0			0
$499$	−15.3614	+	15.3614i	−0.687671	+	0.687671i	−0.961717	−	0.274045i	$-0.911638\pi$
$499$	−15.3614	+	15.3614i	−0.687671	+	0.687671i	0.274045	+	0.961717i	$0.411638\pi$
$500$		0			0
$501$	−11.5575	+	33.3357i	−0.516349	+	1.48933i
$502$		0			0
$503$		−	19.8445i		−	0.884824i	−0.896812	−	0.442412i	$-0.854123\pi$
$503$		−	19.8445i		−	0.884824i	0.896812	−	0.442412i	$-0.145877\pi$
$504$		0			0
$505$		−	1.99092i		−	0.0885949i
$506$		0			0
$507$	7.32747	−	21.1350i	0.325425	−	0.938637i
$508$		0			0
$509$	18.7709	−	18.7709i	0.832006	−	0.832006i	−0.155785	−	0.987791i	$-0.549791\pi$
$509$	18.7709	−	18.7709i	0.832006	−	0.832006i	0.987791	+	0.155785i	$0.0497908\pi$
$510$		0			0
$511$			11.5367i			0.510353i
$512$		0			0
$513$	−42.1595	−	9.24171i	−1.86139	−	0.408031i
$514$		0			0
$515$	0.0755891	+	0.0755891i	0.00333085	+	0.00333085i
$516$		0			0
$517$	−0.431807	+	0.431807i	−0.0189909	+	0.0189909i
$518$		0			0
$519$	6.12464	−	2.97114i	0.268842	−	0.130419i
$520$		0			0
$521$	16.6843			0.730951			0.365476	−	0.930821i	$-0.380906\pi$
$521$	16.6843			0.730951			0.365476	+	0.930821i	$0.380906\pi$
$522$		0			0
$523$	−13.3843	−	13.3843i	−0.585255	−	0.585255i	0.351087	−	0.936343i	$-0.385812\pi$
$523$	−13.3843	−	13.3843i	−0.585255	−	0.585255i	−0.936343	+	0.351087i	$0.885812\pi$
$524$		0			0
$525$	2.81682	−	8.12467i	0.122936	−	0.354590i
$526$		0			0
$527$	17.5027			0.762429
$528$		0			0
$529$	−18.2619			−0.793996
$530$		0			0
$531$	21.0680	−	2.49626i	0.914272	−	0.108328i
$532$		0			0
$533$	1.07110	+	1.07110i	0.0463944	+	0.0463944i
$534$		0			0
$535$	−1.53862			−0.0665203
$536$		0			0
$537$	−8.80219	−	18.1446i	−0.379842	−	0.782998i
$538$		0			0
$539$	−0.715349	+	0.715349i	−0.0308123	+	0.0308123i
$540$		0			0
$541$	0.0442246	+	0.0442246i	0.00190136	+	0.00190136i	0.708057	−	0.706155i	$-0.249572\pi$
$541$	0.0442246	+	0.0442246i	0.00190136	+	0.00190136i	−0.706155	+	0.708057i	$0.749572\pi$
$542$		0			0
$543$	10.8381	−	5.25771i	0.465108	−	0.225630i
$544$		0			0
$545$		−	1.51609i		−	0.0649421i
$546$		0			0
$547$	22.5929	−	22.5929i	0.966004	−	0.966004i	−0.0334367	−	0.999441i	$-0.510645\pi$
$547$	22.5929	−	22.5929i	0.966004	−	0.966004i	0.999441	+	0.0334367i	$0.0106452\pi$
$548$		0			0
$549$	−3.11826	−	26.3175i	−0.133084	−	1.12320i
$550$		0			0
$551$			58.7709i			2.50373i
$552$		0			0
$553$		−	3.48456i		−	0.148179i
$554$		0			0
$555$	2.67539	+	0.927556i	0.113564	+	0.0393726i
$556$		0			0
$557$	−20.6256	+	20.6256i	−0.873935	+	0.873935i	−0.992899	−	0.118964i	$-0.962043\pi$
$557$	−20.6256	+	20.6256i	−0.873935	+	0.873935i	0.118964	+	0.992899i	$0.462043\pi$
$558$		0			0
$559$		−	0.564448i		−	0.0238736i
$560$		0			0
$561$	−5.29236	−	10.9096i	−0.223444	−	0.460602i
$562$		0			0
$563$	2.94590	+	2.94590i	0.124155	+	0.124155i	0.766454	−	0.642299i	$-0.222019\pi$
$563$	2.94590	+	2.94590i	0.124155	+	0.124155i	−0.642299	+	0.766454i	$0.722019\pi$
$564$		0			0
$565$	0.773114	−	0.773114i	0.0325251	−	0.0325251i
$566$		0			0
$567$	2.10322	+	8.75080i	0.0883270	+	0.367499i
$568$		0			0
$569$	−10.0145			−0.419832			−0.209916	−	0.977719i	$-0.567319\pi$
$569$	−10.0145			−0.419832			−0.209916	+	0.977719i	$0.567319\pi$
$570$		0			0
$571$	−14.6624	−	14.6624i	−0.613601	−	0.613601i	0.330282	−	0.943882i	$-0.392856\pi$
$571$	−14.6624	−	14.6624i	−0.613601	−	0.613601i	−0.943882	+	0.330282i	$0.892856\pi$
$572$		0			0
$573$	31.0554	+	10.7669i	1.29736	+	0.449792i
$574$		0			0
$575$	31.8910			1.32995
$576$		0			0
$577$	−1.05507			−0.0439231			−0.0219615	−	0.999759i	$-0.506991\pi$
$577$	−1.05507			−0.0439231			−0.0219615	+	0.999759i	$0.506991\pi$
$578$		0			0
$579$	41.9800	+	14.5544i	1.74463	+	0.604861i
$580$		0			0
$581$	−0.641645	−	0.641645i	−0.0266199	−	0.0266199i
$582$		0			0
$583$	−8.86276			−0.367058
$584$		0			0
$585$	−0.101816	+	0.129187i	−0.00420958	+	0.00534121i
$586$		0			0
$587$	−9.32085	+	9.32085i	−0.384713	+	0.384713i	−0.872797	−	0.488084i	$-0.837696\pi$
$587$	−9.32085	+	9.32085i	−0.384713	+	0.384713i	0.488084	+	0.872797i	$0.337696\pi$
$588$		0			0
$589$	14.8556	+	14.8556i	0.612113	+	0.612113i
$590$		0			0
$591$	−17.5289	−	36.1336i	−0.721042	−	1.48634i
$592$		0			0
$593$			37.6934i			1.54788i	0.633257	+	0.773941i	$0.281717\pi$
$593$			37.6934i			1.54788i	−0.633257	+	0.773941i	$0.718283\pi$
$594$		0			0
$595$	−0.919345	+	0.919345i	−0.0376895	+	0.0376895i
$596$		0			0
$597$	42.5373	+	14.7476i	1.74093	+	0.603580i
$598$		0			0
$599$		−	10.6528i		−	0.435260i	−0.976031	−	0.217630i	$-0.930167\pi$
$599$		−	10.6528i		−	0.435260i	0.976031	−	0.217630i	$-0.0698326\pi$
$600$		0			0
$601$		−	23.0989i		−	0.942224i	−0.882073	−	0.471112i	$-0.843853\pi$
$601$		−	23.0989i		−	0.942224i	0.882073	−	0.471112i	$-0.156147\pi$
$602$		0			0
$603$	−10.7779	+	1.27703i	−0.438910	+	0.0520047i
$604$		0			0
$605$	−1.32542	+	1.32542i	−0.0538860	+	0.0538860i
$606$		0			0
$607$			41.9284i			1.70182i	0.525310	+	0.850911i	$0.323949\pi$
$607$			41.9284i			1.70182i	−0.525310	+	0.850911i	$0.676051\pi$
$608$		0			0
$609$	11.0262	−	5.34895i	0.446804	−	0.216750i
$610$		0			0
$611$	0.124560	+	0.124560i	0.00503914	+	0.00503914i
$612$		0			0
$613$	−31.9233	+	31.9233i	−1.28937	+	1.28937i	−0.354202	+	0.935169i	$0.615247\pi$
$613$	−31.9233	+	31.9233i	−1.28937	+	1.28937i	−0.935169	+	0.354202i	$0.884753\pi$
$614$		0			0
$615$	0.737264	+	1.51978i	0.0297294	+	0.0612834i
$616$		0			0
$617$	−5.95415			−0.239705			−0.119852	−	0.992792i	$-0.538242\pi$
$617$	−5.95415			−0.239705			−0.119852	+	0.992792i	$0.538242\pi$
$618$		0			0
$619$	1.32977	+	1.32977i	0.0534480	+	0.0534480i	0.733326	−	0.679878i	$-0.237967\pi$
$619$	1.32977	+	1.32977i	0.0534480	+	0.0534480i	−0.679878	+	0.733326i	$0.737967\pi$
$620$		0			0
$621$	−28.1079	+	18.0005i	−1.12793	+	0.722336i
$622$		0			0
$623$	11.0057			0.440936
$624$		0			0
$625$	−24.4717			−0.978870
$626$		0			0
$627$	4.76764	−	13.7515i	0.190401	−	0.549183i
$628$		0			0
$629$	42.5772	+	42.5772i	1.69766	+	1.69766i
$630$		0			0
$631$	3.61315			0.143837			0.0719185	−	0.997411i	$-0.477088\pi$
$631$	3.61315			0.143837			0.0719185	+	0.997411i	$0.477088\pi$
$632$		0			0
$633$	30.1785	−	14.6400i	1.19949	−	0.581887i
$634$		0			0
$635$	2.02008	−	2.02008i	0.0801643	−	0.0801643i
$636$		0			0
$637$	0.206350	+	0.206350i	0.00817590	+	0.00817590i
$638$		0			0
$639$	−1.50166	+	1.90535i	−0.0594049	+	0.0753744i
$640$		0			0
$641$			0.330226i			0.0130431i	0.999979	+	0.00652156i	$0.00207589\pi$
$641$			0.330226i			0.0130431i	−0.999979	+	0.00652156i	$0.997924\pi$
$642$		0			0
$643$	−1.15297	+	1.15297i	−0.0454689	+	0.0454689i	−0.729476	−	0.684007i	$-0.760236\pi$
$643$	−1.15297	+	1.15297i	−0.0454689	+	0.0454689i	0.684007	+	0.729476i	$0.260236\pi$
$644$		0			0
$645$	0.206185	−	0.594710i	0.00811854	−	0.0234167i
$646$		0			0
$647$			37.5372i			1.47574i	0.674942	+	0.737871i	$0.264169\pi$
$647$			37.5372i			1.47574i	−0.674942	+	0.737871i	$0.735831\pi$
$648$		0			0
$649$			7.15421i			0.280827i
$650$		0			0
$651$	1.43504	−	4.13916i	0.0562437	−	0.162226i
$652$		0			0
$653$	3.90230	−	3.90230i	0.152709	−	0.152709i	−0.626618	−	0.779327i	$-0.715561\pi$
$653$	3.90230	−	3.90230i	0.152709	−	0.152709i	0.779327	+	0.626618i	$0.215561\pi$
$654$		0			0
$655$		−	1.92919i		−	0.0753796i
$656$		0			0
$657$	−21.4235	+	27.1826i	−0.835809	+	1.06049i
$658$		0			0
$659$	10.7926	+	10.7926i	0.420421	+	0.420421i	0.885349	−	0.464928i	$-0.153920\pi$
$659$	10.7926	+	10.7926i	0.420421	+	0.420421i	−0.464928	+	0.885349i	$0.653920\pi$
$660$		0			0
$661$	−35.6420	+	35.6420i	−1.38631	+	1.38631i	−0.553390	+	0.832922i	$0.686666\pi$
$661$	−35.6420	+	35.6420i	−1.38631	+	1.38631i	−0.832922	+	0.553390i	$0.813334\pi$
$662$		0			0
$663$	−3.14698	+	1.52664i	−0.122219	+	0.0592898i
$664$		0			0
$665$	−1.56061			−0.0605177
$666$		0			0
$667$	32.1379	+	32.1379i	1.24438	+	1.24438i
$668$		0			0
$669$	6.61101	−	19.0685i	0.255597	−	0.737229i
$670$		0			0
$671$	8.93684			0.345003
$672$		0			0
$673$	24.1133			0.929500			0.464750	−	0.885442i	$-0.346144\pi$
$673$	24.1133			0.929500			0.464750	+	0.885442i	$0.346144\pi$
$674$		0			0
$675$	21.7243	−	13.9125i	0.836170	−	0.535491i
$676$		0			0
$677$	9.46846	+	9.46846i	0.363902	+	0.363902i	0.865247	−	0.501345i	$-0.167161\pi$
$677$	9.46846	+	9.46846i	0.363902	+	0.363902i	−0.501345	+	0.865247i	$0.667161\pi$
$678$		0			0
$679$	−5.56394			−0.213525
$680$		0			0
$681$	−0.225603	−	0.465053i	−0.00864514	−	0.0178209i
$682$		0			0
$683$	31.3757	−	31.3757i	1.20056	−	1.20056i	0.226558	−	0.973998i	$-0.427253\pi$
$683$	31.3757	−	31.3757i	1.20056	−	1.20056i	0.973998	−	0.226558i	$-0.0727474\pi$
$684$		0			0
$685$	−0.449220	−	0.449220i	−0.0171638	−	0.0171638i
$686$		0			0
$687$	−25.9390	+	12.5833i	−0.989635	+	0.480085i
$688$		0			0
$689$			2.55656i			0.0973972i
$690$		0			0
$691$	8.64022	−	8.64022i	0.328689	−	0.328689i	−0.523399	−	0.852088i	$-0.675336\pi$
$691$	8.64022	−	8.64022i	0.328689	−	0.328689i	0.852088	+	0.523399i	$0.175336\pi$
$692$		0			0
$693$	−3.01389	+	0.357104i	−0.114488	+	0.0135652i
$694$		0			0
$695$		−	1.63622i		−	0.0620652i
$696$		0			0
$697$			35.9194i			1.36055i
$698$		0			0
$699$	10.2202	+	3.54332i	0.386562	+	0.134021i
$700$		0			0
$701$	−15.8683	+	15.8683i	−0.599338	+	0.599338i	−0.940136	−	0.340798i	$-0.889303\pi$
$701$	−15.8683	+	15.8683i	−0.599338	+	0.599338i	0.340798	+	0.940136i	$0.389303\pi$
$702$		0			0
$703$			72.2757i			2.72593i
$704$		0			0
$705$	0.0857376	+	0.176737i	0.00322906	+	0.00665632i
$706$		0			0
$707$	−7.49292	−	7.49292i	−0.281800	−	0.281800i
$708$		0			0
$709$	0.181876	−	0.181876i	0.00683048	−	0.00683048i	−0.703683	−	0.710514i	$-0.748463\pi$
$709$	0.181876	−	0.181876i	0.00683048	−	0.00683048i	0.710514	+	0.703683i	$0.248463\pi$
$710$		0			0
$711$	6.47078	−	8.21028i	0.242673	−	0.307909i
$712$		0			0
$713$	16.2470			0.608456
$714$		0			0
$715$	−0.0392217	−	0.0392217i	−0.00146681	−	0.00146681i
$716$		0			0
$717$	−42.2958	−	14.6639i	−1.57957	−	0.547634i
$718$		0			0
$719$	−11.0849			−0.413398			−0.206699	−	0.978405i	$-0.566272\pi$
$719$	−11.0849			−0.413398			−0.206699	+	0.978405i	$0.566272\pi$
$720$		0			0
$721$	0.568966			0.0211894
$722$		0			0
$723$	31.0698	+	10.7719i	1.15550	+	0.400611i
$724$		0			0
$725$	−24.8391	−	24.8391i	−0.922500	−	0.922500i
$726$		0			0
$727$	15.6079			0.578864			0.289432	−	0.957199i	$-0.406534\pi$
$727$	15.6079			0.578864			0.289432	+	0.957199i	$0.406534\pi$
$728$		0			0
$729$	−11.2945	+	24.5242i	−0.418315	+	0.908302i
$730$		0			0
$731$	9.46443	−	9.46443i	0.350055	−	0.350055i
$732$		0			0
$733$	28.2446	+	28.2446i	1.04324	+	1.04324i	0.999022	+	0.0442178i	$0.0140796\pi$
$733$	28.2446	+	28.2446i	1.04324	+	1.04324i	0.0442178	+	0.999022i	$0.485920\pi$
$734$		0			0
$735$	0.142036	+	0.292790i	0.00523909	+	0.0107997i
$736$		0			0
$737$		−	3.65994i		−	0.134815i
$738$		0			0
$739$	29.2990	−	29.2990i	1.07778	−	1.07778i	0.0810730	−	0.996708i	$-0.474165\pi$
$739$	29.2990	−	29.2990i	1.07778	−	1.07778i	0.996708	−	0.0810730i	$-0.0258347\pi$
$740$		0			0
$741$	−3.96678	−	1.37528i	−0.145723	−	0.0505221i
$742$		0			0
$743$		−	27.2593i		−	1.00005i	−0.866012	−	0.500023i	$-0.833325\pi$
$743$		−	27.2593i		−	1.00005i	0.866012	−	0.500023i	$-0.166675\pi$
$744$		0			0
$745$			0.948752i			0.0347596i
$746$		0			0
$747$	−0.320310	−	2.70336i	−0.0117195	−	0.0989107i
$748$		0			0
$749$	−5.79066	+	5.79066i	−0.211586	+	0.211586i
$750$		0			0
$751$		−	40.8770i		−	1.49162i	−0.666157	−	0.745811i	$-0.732062\pi$
$751$		−	40.8770i		−	1.49162i	0.666157	−	0.745811i	$-0.267938\pi$
$752$		0			0
$753$	23.3030	−	11.3046i	0.849207	−	0.411961i
$754$		0			0
$755$	0.306219	+	0.306219i	0.0111444	+	0.0111444i
$756$		0			0
$757$	11.5259	−	11.5259i	0.418914	−	0.418914i	−0.465915	−	0.884829i	$-0.654275\pi$
$757$	11.5259	−	11.5259i	0.418914	−	0.418914i	0.884829	+	0.465915i	$0.154275\pi$
$758$		0			0
$759$	−4.91268	−	10.1269i	−0.178319	−	0.367583i
$760$		0			0
$761$	27.9488			1.01314			0.506572	−	0.862198i	$-0.330913\pi$
$761$	27.9488			1.01314			0.506572	+	0.862198i	$0.330913\pi$
$762$		0			0
$763$	−5.70587	−	5.70587i	−0.206566	−	0.206566i
$764$		0			0
$765$	−3.87336	+	0.458939i	−0.140042	+	0.0165930i
$766$		0			0
$767$	2.06371			0.0745162
$768$		0			0
$769$	−33.1252			−1.19453			−0.597263	−	0.802046i	$-0.703745\pi$
$769$	−33.1252			−1.19453			−0.597263	+	0.802046i	$0.703745\pi$
$770$		0			0
$771$	−2.45075	+	7.06881i	−0.0882616	+	0.254577i
$772$		0			0
$773$	25.5398	+	25.5398i	0.918603	+	0.918603i	0.996928	−	0.0783250i	$-0.0249572\pi$
$773$	25.5398	+	25.5398i	0.918603	+	0.918603i	−0.0783250	+	0.996928i	$0.524957\pi$
$774$		0			0
$775$	−12.5572			−0.451067
$776$		0			0
$777$	13.5599	−	6.57806i	0.486457	−	0.235987i
$778$		0			0
$779$	−30.4870	+	30.4870i	−1.09231	+	1.09231i
$780$		0			0
$781$	−0.578473	−	0.578473i	−0.0206994	−	0.0206994i
$782$		0			0
$783$	35.9127	+	7.87235i	1.28341	+	0.281335i
$784$		0			0
$785$		−	3.21295i		−	0.114675i
$786$		0			0
$787$	−15.0726	+	15.0726i	−0.537282	+	0.537282i	−0.922730	−	0.385448i	$-0.874047\pi$
$787$	−15.0726	+	15.0726i	−0.537282	+	0.537282i	0.385448	+	0.922730i	$0.374047\pi$
$788$		0			0
$789$	−6.78896	+	19.5817i	−0.241693	+	0.697128i
$790$		0			0
$791$		−	5.81929i		−	0.206910i
$792$		0			0
$793$		−	2.57793i		−	0.0915450i
$794$		0			0
$795$	−0.933877	+	2.69362i	−0.0331212	+	0.0955330i
$796$		0			0
$797$	−22.0934	+	22.0934i	−0.782588	+	0.782588i	−0.980267	−	0.197679i	$-0.936660\pi$
$797$	−22.0934	+	22.0934i	−0.782588	+	0.782588i	0.197679	+	0.980267i	$0.436660\pi$
$798$		0			0
$799$			4.17712i			0.147776i
$800$		0			0
$801$	25.9316	+	20.4375i	0.916247	+	0.722123i
$802$		0			0
$803$	−8.25277	−	8.25277i	−0.291234	−	0.291234i
$804$		0			0
$805$	−0.853390	+	0.853390i	−0.0300781	+	0.0300781i
$806$		0			0
$807$	−42.9656	+	20.8432i	−1.51246	+	0.733715i
$808$		0			0
$809$	0.787723			0.0276949			0.0138474	−	0.999904i	$-0.495592\pi$
$809$	0.787723			0.0276949			0.0138474	+	0.999904i	$0.495592\pi$
$810$		0			0
$811$	−2.79456	−	2.79456i	−0.0981301	−	0.0981301i	0.656337	−	0.754468i	$-0.272105\pi$
$811$	−2.79456	−	2.79456i	−0.0981301	−	0.0981301i	−0.754468	+	0.656337i	$0.772105\pi$
$812$		0			0
$813$	−2.72341	+	7.85527i	−0.0955142	+	0.275496i
$814$		0			0
$815$	0.288925			0.0101206
$816$		0			0
$817$	16.0661			0.562080
$818$		0			0
$819$	0.103010	+	0.869389i	0.00359947	+	0.0303789i
$820$		0			0
$821$	2.46211	+	2.46211i	0.0859283	+	0.0859283i	0.748764	−	0.662836i	$-0.230647\pi$
$821$	2.46211	+	2.46211i	0.0859283	+	0.0859283i	−0.662836	+	0.748764i	$0.730647\pi$
$822$		0			0
$823$	40.9038			1.42582			0.712908	−	0.701258i	$-0.247378\pi$
$823$	40.9038			1.42582			0.712908	+	0.701258i	$0.247378\pi$
$824$		0			0
$825$	3.79697	+	7.82698i	0.132194	+	0.272501i
$826$		0			0
$827$	−12.8277	+	12.8277i	−0.446061	+	0.446061i	−0.894043	−	0.447982i	$-0.852143\pi$
$827$	−12.8277	+	12.8277i	−0.446061	+	0.446061i	0.447982	+	0.894043i	$0.352143\pi$
$828$		0			0
$829$	−0.182463	−	0.182463i	−0.00633720	−	0.00633720i	0.703931	−	0.710268i	$-0.251426\pi$
$829$	−0.182463	−	0.182463i	−0.00633720	−	0.00633720i	−0.710268	+	0.703931i	$0.751426\pi$
$830$		0			0
$831$	35.6970	−	17.3171i	1.23831	−	0.600722i
$832$		0			0
$833$			6.91999i			0.239763i
$834$		0			0
$835$	−2.70626	+	2.70626i	−0.0936541	+	0.0936541i
$836$		0			0
$837$	11.0676	−	7.08778i	0.382551	−	0.244989i
$838$		0			0
$839$			4.28148i			0.147813i	0.997265	+	0.0739065i	$0.0235466\pi$
$839$			4.28148i			0.147813i	−0.997265	+	0.0739065i	$0.976453\pi$
$840$		0			0
$841$		−	21.0628i		−	0.726302i
$842$		0			0
$843$	−26.7076	−	9.25951i	−0.919859	−	0.318914i
$844$		0			0
$845$	1.71578	−	1.71578i	0.0590247	−	0.0590247i
$846$		0			0
$847$			9.97655i			0.342798i
$848$		0			0
$849$	−17.4862	−	36.0456i	−0.600124	−	1.23708i
$850$		0			0
$851$	39.5227	+	39.5227i	1.35482	+	1.35482i
$852$		0			0
$853$	28.0775	−	28.0775i	0.961357	−	0.961357i	−0.0379241	−	0.999281i	$-0.512075\pi$
$853$	28.0775	−	28.0775i	0.961357	−	0.961357i	0.999281	+	0.0379241i	$0.0120745\pi$
$854$		0			0
$855$	−3.67708	−	2.89802i	−0.125753	−	0.0991103i
$856$		0			0
$857$	−7.48369			−0.255638			−0.127819	−	0.991798i	$-0.540798\pi$
$857$	−7.48369			−0.255638			−0.127819	+	0.991798i	$0.540798\pi$
$858$		0			0
$859$	8.72002	+	8.72002i	0.297523	+	0.297523i	0.840043	−	0.542520i	$-0.182530\pi$
$859$	8.72002	+	8.72002i	0.297523	+	0.297523i	−0.542520	+	0.840043i	$0.682530\pi$
$860$		0			0
$861$	8.49448	+	2.94503i	0.289491	+	0.100366i
$862$		0			0
$863$	44.3294			1.50899			0.754495	−	0.656306i	$-0.227882\pi$
$863$	44.3294			1.50899			0.754495	+	0.656306i	$0.227882\pi$
$864$		0			0
$865$	0.738415			0.0251069
$866$		0			0
$867$	−50.5450	−	17.5239i	−1.71660	−	0.595143i
$868$		0			0
$869$	2.49268	+	2.49268i	0.0845584	+	0.0845584i
$870$		0			0
$871$	−1.05575			−0.0357727
$872$		0			0
$873$	−13.1097	−	10.3322i	−0.443696	−	0.349690i
$874$		0			0
$875$	1.32385	−	1.32385i	0.0447542	−	0.0447542i
$876$		0			0
$877$	16.9604	+	16.9604i	0.572712	+	0.572712i	0.932885	−	0.360173i	$-0.117282\pi$
$877$	16.9604	+	16.9604i	0.572712	+	0.572712i	−0.360173	+	0.932885i	$0.617282\pi$
$878$		0			0
$879$	5.13544	+	10.5861i	0.173214	+	0.357060i
$880$		0			0
$881$		−	24.9798i		−	0.841590i	−0.907156	−	0.420795i	$-0.861751\pi$
$881$		−	24.9798i		−	0.841590i	0.907156	−	0.420795i	$-0.138249\pi$
$882$		0			0
$883$	−12.8228	+	12.8228i	−0.431520	+	0.431520i	−0.889145	−	0.457625i	$-0.848700\pi$
$883$	−12.8228	+	12.8228i	−0.431520	+	0.431520i	0.457625	+	0.889145i	$0.348700\pi$
$884$		0			0
$885$	2.17435	+	0.753845i	0.0730900	+	0.0253402i
$886$		0			0
$887$			6.33001i			0.212541i	0.994337	+	0.106270i	$0.0338909\pi$
$887$			6.33001i			0.212541i	−0.994337	+	0.106270i	$0.966109\pi$
$888$		0			0
$889$		−	15.2053i		−	0.509969i
$890$		0			0
$891$	−7.76441	−	4.75534i	−0.260118	−	0.159310i
$892$		0			0
$893$	−3.54538	+	3.54538i	−0.118641	+	0.118641i
$894$		0			0
$895$		−	2.18760i		−	0.0731233i
$896$		0			0
$897$	−2.92121	+	1.41712i	−0.0975364	+	0.0473162i
$898$		0			0
$899$	−12.6544	−	12.6544i	−0.422048	−	0.422048i
$900$		0			0
$901$	−42.8673	+	42.8673i	−1.42812	+	1.42812i
$902$		0			0
$903$	−1.46223	−	3.01420i	−0.0486599	−	0.100306i
$904$		0			0
$905$	1.30669			0.0434360
$906$		0			0
$907$	−26.3398	−	26.3398i	−0.874598	−	0.874598i	0.118371	−	0.992969i	$-0.462233\pi$
$907$	−26.3398	−	26.3398i	−0.874598	−	0.874598i	−0.992969	+	0.118371i	$0.962233\pi$
$908$		0			0
$909$	−3.74048	−	31.5690i	−0.124064	−	1.04708i
$910$		0			0
$911$	−14.6002			−0.483727			−0.241864	−	0.970310i	$-0.577759\pi$
$911$	−14.6002			−0.483727			−0.241864	+	0.970310i	$0.577759\pi$
$912$		0			0
$913$	0.918000			0.0303814
$914$		0			0
$915$	0.941683	−	2.71614i	0.0311311	−	0.0897928i
$916$		0			0
$917$	−7.26058	−	7.26058i	−0.239765	−	0.239765i
$918$		0			0
$919$	−48.0819			−1.58608			−0.793039	−	0.609171i	$-0.791502\pi$
$919$	−48.0819			−1.58608			−0.793039	+	0.609171i	$0.791502\pi$
$920$		0			0
$921$	−5.67133	+	2.75124i	−0.186877	+	0.0906563i
$922$		0			0
$923$	−0.166867	+	0.166867i	−0.00549248	+	0.00549248i
$924$		0			0
$925$	−30.5467	−	30.5467i	−1.00437	−	1.00437i
$926$		0			0
$927$	1.34059	+	1.05656i	0.0440307	+	0.0347020i
$928$		0			0
$929$		−	8.27555i		−	0.271512i	−0.990742	−	0.135756i	$-0.956654\pi$
$929$		−	8.27555i		−	0.271512i	0.990742	−	0.135756i	$-0.0433463\pi$
$930$		0			0
$931$	−5.87341	+	5.87341i	−0.192493	+	0.192493i
$932$		0			0
$933$	9.54281	−	27.5248i	0.312417	−	0.901120i
$934$		0			0
$935$		−	1.31531i		−	0.0430151i
$936$		0			0
$937$			55.6179i			1.81696i	0.417933	+	0.908478i	$0.362755\pi$
$937$			55.6179i			1.81696i	−0.417933	+	0.908478i	$0.637245\pi$
$938$		0			0
$939$	1.75577	−	5.06425i	0.0572974	−	0.165266i
$940$		0			0
$941$	39.8696	−	39.8696i	1.29971	−	1.29971i	0.371134	−	0.928579i	$-0.378969\pi$
$941$	39.8696	−	39.8696i	1.29971	−	1.29971i	0.928579	−	0.371134i	$-0.121031\pi$
$942$		0			0
$943$			33.3425i			1.08578i
$944$		0			0
$945$	−0.209043	+	0.953627i	−0.00680016	+	0.0310215i
$946$		0			0
$947$	−25.0837	−	25.0837i	−0.815110	−	0.815110i	0.170285	−	0.985395i	$-0.445531\pi$
$947$	−25.0837	−	25.0837i	−0.815110	−	0.815110i	−0.985395	+	0.170285i	$0.945531\pi$
$948$		0			0
$949$	−2.38060	+	2.38060i	−0.0772776	+	0.0772776i
$950$		0			0
$951$	−25.9450	+	12.5862i	−0.841323	+	0.408137i
$952$		0			0
$953$	42.9272			1.39055			0.695274	−	0.718745i	$-0.255283\pi$
$953$	42.9272			1.39055			0.695274	+	0.718745i	$0.255283\pi$
$954$		0			0
$955$	2.52114	+	2.52114i	0.0815822	+	0.0815822i
$956$		0			0
$957$	−4.06121	+	11.7139i	−0.131280	+	0.378658i
$958$		0			0
$959$	−3.38132			−0.109188
$960$		0			0
$961$	24.6027			0.793635
$962$		0			0
$963$	−24.3970	+	2.89071i	−0.786183	+	0.0931517i
$964$		0			0
$965$	3.40803	+	3.40803i	0.109708	+	0.109708i
$966$		0			0
$967$	−40.4433			−1.30057			−0.650285	−	0.759690i	$-0.725350\pi$
$967$	−40.4433			−1.30057			−0.650285	+	0.759690i	$0.725350\pi$
$968$		0			0
$969$	−43.4532	−	89.5734i	−1.39592	−	2.87751i
$970$		0			0
$971$	−30.5811	+	30.5811i	−0.981394	+	0.981394i	−0.999830	−	0.0184358i	$-0.994131\pi$
$971$	−30.5811	+	30.5811i	−0.981394	+	0.981394i	0.0184358	+	0.999830i	$0.494131\pi$
$972$		0			0
$973$	−6.15797	−	6.15797i	−0.197415	−	0.197415i
$974$		0			0
$975$	2.25778	−	1.09528i	0.0723068	−	0.0350770i
$976$		0			0
$977$		−	3.04304i		−	0.0973554i	−0.998815	−	0.0486777i	$-0.984499\pi$
$977$		−	3.04304i		−	0.0973554i	0.998815	−	0.0486777i	$-0.0155007\pi$
$978$		0			0
$979$	−7.87295	+	7.87295i	−0.251621	+	0.251621i
$980$		0			0
$981$	−2.84838	−	24.0398i	−0.0909417	−	0.767531i
$982$		0			0
$983$		−	50.6697i		−	1.61611i	−0.589106	−	0.808056i	$-0.700520\pi$
$983$		−	50.6697i		−	1.61611i	0.589106	−	0.808056i	$-0.299480\pi$
$984$		0			0
$985$		−	4.35643i		−	0.138808i
$986$		0			0
$987$	0.987836	+	0.342482i	0.0314432	+	0.0109013i
$988$		0			0
$989$	8.78544	−	8.78544i	0.279361	−	0.279361i
$990$		0			0
$991$		−	12.2969i		−	0.390623i	−0.980741	−	0.195311i	$-0.937428\pi$
$991$		−	12.2969i		−	0.390623i	0.980741	−	0.195311i	$-0.0625717\pi$
$992$		0			0
$993$	15.9204	+	32.8180i	0.505220	+	1.04145i
$994$		0			0
$995$	3.45326	+	3.45326i	0.109476	+	0.109476i
$996$		0			0
$997$	−17.3109	+	17.3109i	−0.548242	+	0.548242i	−0.925932	−	0.377690i	$-0.876719\pi$
$997$	−17.3109	+	17.3109i	−0.548242	+	0.548242i	0.377690	+	0.925932i	$0.376719\pi$
$998$		0			0
$999$	44.1649	+	9.68130i	1.39732	+	0.306303i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.s.c.239.18		40
3.2	odd	2	inner	1344.2.s.c.239.9		40
4.3	odd	2		336.2.s.c.323.3	yes	40
12.11	even	2		336.2.s.c.323.18	yes	40
16.5	even	4		336.2.s.c.155.18	yes	40
16.11	odd	4	inner	1344.2.s.c.911.9		40
48.5	odd	4		336.2.s.c.155.3	✓	40
48.11	even	4	inner	1344.2.s.c.911.18		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.c.155.3	✓	40	48.5	odd	4
336.2.s.c.155.18	yes	40	16.5	even	4
336.2.s.c.323.3	yes	40	4.3	odd	2
336.2.s.c.323.18	yes	40	12.11	even	2
1344.2.s.c.239.9		40	3.2	odd	2	inner
1344.2.s.c.239.18		40	1.1	even	1	trivial
1344.2.s.c.911.9		40	16.11	odd	4	inner
1344.2.s.c.911.18		40	48.11	even	4	inner

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:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.63649 + 0.567369i) q^{3} +(0.132854 + 0.132854i) q^{5} +1.00000 q^{7} +(2.35619 + 1.85698i) q^{9} +O(q^{10})\)	\(q+(1.63649 + 0.567369i) q^{3} +(0.132854 + 0.132854i) q^{5} +1.00000 q^{7} +(2.35619 + 1.85698i) q^{9} +(-0.715349 + 0.715349i) q^{11} +(0.206350 + 0.206350i) q^{13} +(0.142036 + 0.292790i) q^{15} +6.91999i q^{17} +(-5.87341 + 5.87341i) q^{19} +(1.63649 + 0.567369i) q^{21} +6.42354i q^{23} -4.96470i q^{25} +(2.80227 + 4.37576i) q^{27} +(5.00314 - 5.00314i) q^{29} -2.52929i q^{31} +(-1.57653 + 0.764794i) q^{33} +(0.132854 + 0.132854i) q^{35} +(6.15279 - 6.15279i) q^{37} +(0.220613 + 0.454766i) q^{39} +5.19068 q^{41} +(-1.36769 - 1.36769i) q^{43} +(0.0663207 + 0.559735i) q^{45} +0.603632 q^{47} +1.00000 q^{49} +(-3.92619 + 11.3245i) q^{51} +(6.19471 + 6.19471i) q^{53} -0.190073 q^{55} +(-12.9442 + 6.27938i) q^{57} +(5.00050 - 5.00050i) q^{59} +(-6.24649 - 6.24649i) q^{61} +(2.35619 + 1.85698i) q^{63} +0.0548287i q^{65} +(-2.55815 + 2.55815i) q^{67} +(-3.64452 + 10.5120i) q^{69} +0.808658i q^{71} +11.5367i q^{73} +(2.81682 - 8.12467i) q^{75} +(-0.715349 + 0.715349i) q^{77} -3.48456i q^{79} +(2.10322 + 8.75080i) q^{81} +(-0.641645 - 0.641645i) q^{83} +(-0.919345 + 0.919345i) q^{85} +(11.0262 - 5.34895i) q^{87} +11.0057 q^{89} +(0.206350 + 0.206350i) q^{91} +(1.43504 - 4.13916i) q^{93} -1.56061 q^{95} -5.56394 q^{97} +(-3.01389 + 0.357104i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} + 40 q^{7}+O(q^{10}) \) 40 * q - 4 * q^3 + 40 * q^7	\( 40 q - 4 q^{3} + 40 q^{7} + 24 q^{13} - 16 q^{19} - 4 q^{21} + 32 q^{27} + 24 q^{33} - 8 q^{37} + 64 q^{39} - 24 q^{43} - 28 q^{45} + 40 q^{49} + 32 q^{51} - 16 q^{55} - 48 q^{61} - 40 q^{67} + 4 q^{69} - 40 q^{75} + 56 q^{81} - 48 q^{85} - 32 q^{87} + 24 q^{91} + 56 q^{93} + 16 q^{97} - 24 q^{99}+O(q^{100}) \) 40 * q - 4 * q^3 + 40 * q^7 + 24 * q^13 - 16 * q^19 - 4 * q^21 + 32 * q^27 + 24 * q^33 - 8 * q^37 + 64 * q^39 - 24 * q^43 - 28 * q^45 + 40 * q^49 + 32 * q^51 - 16 * q^55 - 48 * q^61 - 40 * q^67 + 4 * q^69 - 40 * q^75 + 56 * q^81 - 48 * q^85 - 32 * q^87 + 24 * q^91 + 56 * q^93 + 16 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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